As you can see, some of the ‘evidence’ of an officer’s suicide is of dubious nature, at the least. The survivor’s accounts disagree with each other, and some of the survivors couldn’t have seen what they said they did. However, the dubious nature of some of the accounts does not automatically disprove them, either.
But we do see some consistency! Many of the accounts above, refer to events on the starboard Boat Deck, not long before the Bridge area dipped under. There are two first hand witnesses, both of whom would have been in the correct place to witness a suicide, and both of whom gave multiple accounts of the shooting/suicide: Eugene Daly and George Rheims. Their statements, coupled with those of other people who gave press accounts claiming to have witnessed a suicide, and were in the correct position to have witnessed it (Dorking, Jansson, etc.), strongly suggests that the story may indeed have a basis in fact.
In the following section, the possible motivation of the various ‘suspects’ is addressed. Please keep in mind – this is speculation only! There is no way to actually ‘know’ what was going through these men’s minds in the final stages of the sinking.
Certain motivations were common to all these men – the imminent sinking of the ship, and death of most of those still on the ship, including the officer himself. Also – was this unknown officer involved in any passengers being shot, as some of the accounts say?
Captain Edward John Smith
      
       As shown above in some of the accounts themselves, Captain
      Smith was mentioned as having shot himself at the end.  Other
      accounts have Smith diving overboard from the bridge, or even
      going inside the wheelhouse (as he did in the Cameron movie). 
Possible Motivation 
        Captain Smith was the man ultimately responsible for the Titanic
        – and her passengers.  Regardless of whether he was on the
        bridge during the collision, he was responsible.  Even
        though he was due to retire soon, the sinking of the Titanic
        would be a very large blemish on his reputation. 
        Location 
        A number of accounts have Smith on the forward areas of the Boat
        Deck, near to the Bridge, not long before she dipped
        under.  Bride’s account even has him diving off the Bridge
        as she dipped under.  He seems to have been close to the
        areas usually associated with an officer’s suicide. 
        The Means 
        Captain Smith was one of the officers who went to the Chief
        Officer’s cabin when the revolvers were brought out and
        distributed (Lightoller’s Titanic and Other Ships).
Chief Officer Henry Wilde
      
       In all the survivor accounts available at this time
      detailing an officer’s suicide, the very few mentions of Henry
      Wilde by name are not very convincing.  The above listed
      account by "Unknown" could easily have been a fabrication by a
      reporter, the mention of Wilde in the Hyman headline may also be a
      reporter's fabrication, as Hyman himself does not mention Wilde in
      the account.  Yes, the name “Chief Officer” is mentioned in a
      number of accounts, but as detailed earlier, the fact is that not
      all survivor’s meant Wilde when using that term. Any references to
      the Chief Officer shooting himself, apply equally as well to
      Murdoch as they would to Wilde. 
Possible Motivation 
        It has been suggested that Wilde could have been despondent over
        the death of his wife, and that the disaster of the Titanic
        pushed him over the edge into suicide.  However, the death
        of his wife and two sons had occurred almost a  year and a
        half before he shipped out on the Titanic.  Wilde also had
        4 surviving children waiting for him at home, depending on him
        for continuing support. 
Second Officer Lightoller, in the article he wrote for The Christian Science Journal (Vol. XXX, 10/1912, No. 7), stated "[I] was on my way back on deck again when I heard Wilde say, 'I am going to put on my life-belt.'" At this time that Lightoller saw Wilde, it does not appear that Wilde was suicidal, although this could have changed in the last minutes.
Location 
        When last seen, Wilde was helping load the forward boats – he
        was there for both Collapsibles C and D.  Since C was
        lowered slightly before D, Wilde would have had to cross over to
        the port side.  No eyewitness testimony has been found
        which shows he crossed back to the starboard side. 
        However, it does seem very likely that he would have stayed in
        the bridge area, and continued trying to help up until the end.
        
        The Means 
        Wilde probably did have a weapon that night, in fact, it was
        Wilde himself who asked for the weapons to be brought out and
        distributed.
First Officer William Murdoch
      
       Murdoch is usually the officer mentioned, by name, when
      detailing who may have shot himself as the ship sank.  This
      in itself does not ‘prove’ it was Murdoch; however, it does lend a
      bit more weight to the assertion, than it does to the other
      suspects. However, any references to the Chief Officer shooting
      himself, apply just as well to Murdoch as they would to Wilde. 
Possible Motivation 
        Murdoch was the man directly in charge of the ship in the hours
        leading up to the collision with the iceberg.  As such, he
        was responsible for the ship and all its passengers during that
        time.  His career at sea was effectively over, if he
        survived the disaster. 
If ‘the’ iceberg was not the first to be spotted that night, as brought out in George Behe’s Titanic: Safety, Speed and Sacrifice, then Murdoch was also responsible for not slowing down, in direct violation of the posted orders from the White Star Line, that “Time must be sacrificed or any other temporary inconvenience suffered, rather than the lightest risk should be incurred.” He also did not follow Captain Smith’s final orders (passed on from Lightoller), to "If in the slightest degree doubtful, let me know."
Like Wilde, Murdoch also had family at home dependent on him -
        his wife Ada.  Ada, though having lived in England for a
        number of years, was actually from New Zealand. 
        Location 
        Murdoch was right where many of the suicide accounts place the
        shooting – at the forward lifeboat station on the starboard
        side. 
        The Means 
        Murdoch was one of the officers who could have received one of
        the revolvers when they were passed out in the Chief Officer’s
        cabin earlier that evening.
Purser Herbert McElroy 
      Though not noted in 1912, McElroy was seen on in the general area
      the suicide supposedly happened in, and was also seen to fire a
      revolver (according to Thayer, 1932 and 1940).  Other than
      that, there is no reason to suppose he would have shot himself. 
Possible Motivation 
        Other than realizing the imminent sinking of the ship, and the
        death of many on board the ship, including himself, McElroy had
        no special reasons to commit suicide. 
        Location 
        According to Jack Thayer’s 1940 account, McElroy was helping to
        load Collapsible C from A deck, shortly before the bridge dipped
        under (no 1912 accounts exist placing McElroy in this area,
        however).  Thayer's 1932 account also places McElroy on the
        forward starboard side of the ship.  If this actually was
        McElroy (see William Ward's statement, under "Why
            were officers sometimes mis-identified?" above,
        it seems likely that he would have remained in this same general
        area, but transferred up to the Boat Deck, to help with
        Collapsible A.  However, this is speculation only – there
        have been no reports of McElroy being seen after this sighting
        at C. 
        The Means 
        It is unknown how or why McElroy would have had a weapon in his
        position.  He was not part of the group that was in the
        Chief Officer’s cabin when revolvers were handed out, and his
        position as Purser would not have made it likely for him to have
        a weapon.
Of all the people who are thought of as possible suicides, McElroy is the only one whose body was recovered. The Mackay-Bennett picked the body up on April 23rd (a week after the disaster). Listed as #157, the body was buried at sea.
No statement was ever released saying McElroy’s body did or did not have a gunshot wound, though Sinking of the Titanic by Jay Henry Mowbray mentions a statement attributed to Capt. Lardner and the crew of the Mackay-Bennett that "not one of the bodies that were recovered had any pistol shots".
Sixth Officer James Moody
      
      Really, the only ‘evidence’ for suspecting Moody as the suicide
      victim, is that he was seen on the forward starboard boat deck, at
      around the same time as the supposed suicide. 
Possible Motivation 
        Moody had no special reasons to kill himself that we know of,
        other than realizing he was likely to die in the freezing water
        as the ship sank. 
        Location 
        According to Sam Hemming's account at the US Inquiry, Moody is
        reported to have been helping at Collapsible A as the bridge
        dipped under – the same place as Murdoch .
        The Means 
        He was not part of the group that was in the Chief Officer’s
        cabin to receive a weapon.  There is no evidence that Moody
        did have a gun that night, though it is possible that a gun was
        passed to him by Wilde or someone else.  This is not proof
        that he had one, however.
Chief Engineer Joseph Bell
      
      There is absolutely no reason to consider Bell a “suspect” as the
      person who committed suicide, other than press accounts mentioning
      that he was rumored to have shot himself. On April 19th, 1912,
      both the New York Times and the New York Herald
      printed this, but the source of these allegations was not given.
      Bell’s body was not recovered. 
Possible Motivation 
        No specific motivation can be determined. x
        Location 
        The last sighting of Bell may have been by Second Officer
        Lightoller, after Boat No. 4 was lowered away at 1:50 a.m.
        Writing 23 years after the disaster, Lightoller said that he saw
        all of the engineers after they came up on deck. They had been
        released from their duty so that they could take their chances
        up on deck (Lightoller's Titanic & Other Ships,
        1935). This would mesh pretty well with other available
        statements about men from the Engineering Department and at
        least one engineer being seen on the deck by other survivors.
        However, this it also clashes with Lightoller’s 1912 testimony,
        in which he specifically denied having seen the engineers on
        deck (British Inquiry 14565-14568). 
        The Means 
        There is no evidence that Chief Engineer Bell had a firearm. 
Other than the rumors in the press, there is absolutely no reason to believe that Chief Engineer Bell shot himself. No actual eyewitness accounts claiming that he shot himself have surfaced.
Master-at-Arms Thomas W. King
      
      Some researchers have suggested that it might have been King who
      committed suicide. There is absolutely no evidence to suggest
      this. His body was not recovered. 
Possible Motivation 
        No specific motivation can be determined. 
        Location 
        King’s location during the loading of the collapsibles and
        during the sinking in general is unknown. 
        The Means 
        It is unknown whether or not King’s position as Master-at-Arms
        would have required him to have a firearm. 
First Class passenger Major
        Archibald Butt 
      One of the more wild press rumors was that Major Butt had entered
      into an agreement with fellow First Class passengers George W.
      Widener, Colonel Astor, and Isidor Strauss to kill them first,
      then shoot himself before the boat sank, and that this act had
      been carried out (published in the New York Times, April
      19, 1912). Butt and Widener’s bodies were not recovered, but
      Astor’s and Straus’ were. No mentions of gunshot wounds were made
      (Record of Bodies and Effects: Passengers and Crew, S.S.
        Titanic, Nos. 124 & 96, Public Archives of Nova Scotia).
      Quotes attributed to a male Second Class passenger, most likely
      Albert Caldwell (New York Herald, April 19, 1912), and to
      Mrs. Henry B. Harris (The Sinking of the Titanic, by Logan
      Marshall, 1912), claim that Major Butt helped keep men from
      rushing the lifeboats at gunpoint, and according to the former,
      may have even opened fired on them. Mrs. Harris later denied that
      Major Butt had fired a shot (Omaha Daily News, April 21,
      1912). Caldwell was rescued in Boat No. 13 along with his wife and
      10 month old son, too long before the sinking and on the wrong
      side of the ship to have seen Butt, and Mrs. Harris was rescued in
      Collapsible D, where she *could* have seen something. It is
      plausible that if Major Butt was wearing his military uniform, and
      that he could have been mistaken for an officer.  
    
Possible Motivation 
        No specific motivation can be determined. 
        Location 
        Archibald Butt appears to have been last seen during the
        launching of Collapsible D around 2:05 a.m., where shots may
        have been fired, and one of the locations where a suicide could
        potentially have taken place, based on the eyewitness accounts.
        The Means 
        Besides the questionable newspaper accounts, there is no reason
        to suspect that Major Butt had a firearm or committed suicide. 
The Denver Post of April 19th, 1912, published the following drawing, showing Major Butt holding "the frantic men at bay, as the women got into the boats". Though it doesn't specifically indicate a suicide, it does seem to illustrate the accounts of Caldwell and Harris, and the perception that Major Butt did use his pistol that night.

    
Note:
One very important thing to remember when considering this subject is that there is no solid evidence whatsoever that any bodies were recovered with gunshot wounds. In a 1912 press account, an unnamed Carpathia passenger stated that one of the bodies brought onboard the ship after the survivors were rescued was a fireman who had been “shot by one of the officers for disobeying orders” and pushing into the last boat ahead of the women and children. There is absolutely no eyewitness testimony which backs up this claim.There are also stories that John Snow, a Halifax undertaker who worked on some of the Titanic victims, may have seen evidence of gunshot wounds on the some of the recovered victims (Titanic: Touchstones of a Tragedy: The Timeless Human Drama Revisited through Period Artifacts and Memorabilia, by Steve Santini, 2000). This report cannot be substantiated, however, and is second- or third-hand at best. Even if there were passengers who were shot, or even if an officer committed suicide, the odds that their bodies were recovered are highly unlikely. Only 337 out of the 1,496 victims’ bodies were recovered (23%) (See Bill Wormstedt’s article “An Analysis of the Bodies Recovered from Titanic,” at the following URL: http://www.wormstedt.com/Titanic/analysis.html). Captain Lardner of the Mackay-Bennett, the ship that recovered the bodies, stated that “not one of the bodies that were recovered had any pistol shots" (The Sinking of the Titanic, by Jay Henry Mowbray, 1912).”
Alternative Explanations?
Some Titanic researchers have theorized that nobody shot anyone or committed suicide, but that there is another way of explaining the eyewitness accounts: when Titanic’s forward funnel fell, the wire stays supporting it snapped, sounding like gunshots, and the flying wires cut passengers down, fooling nearby witnesses into believing that the victims had been shot.
While this is an interesting theory and could explain the accounts of those who merely heard noises that they believed were gunfire, it does not explain the accounts of passengers such as Eugene Daly, George Rheims and others who were nearby and claim to have seen the shooting occur during the loading and lowering of a lifeboat. If Richard Norris Williams’ account is accurate, it would seem to make the snapping funnel stay theory even less likely, since the gunfire that he heard occurred well before his father was killed by the falling forward funnel.
Another theory that has been put forward is that witnesses saw or heard Fifth Officer Lowe fire warning shots at Boat No. 14, and due to the confusion, believed that passengers were actually being fired upon. However, this does not explain the accounts of those who heard shots fired shortly before, or right as the Boat Deck plunged under. Boat No. 14 was launched at 1:25 a.m., while the Boat Deck plunged under fifty minutes later, around 2:15 a.m.
This theory also does not adequately explain the accounts of those who said they actually saw a shooting right near them, or who, like Daly, saw the bodies lying on the deck. The timing of the shots at No. 14 does not match that of the gunfire described by witnesses, many of whom place the alleged shooting/suicide late in the loading and lowering of either Collapsible C or D, or during the attempted launch of Collapsible A.