James Bond (Sean Connery) carries a Walther PPK in .32 ACP as his personal sidearm. Kerim Bey (Pedro Armendariz), head of MI-6's "Station T" in Turkey, also carries a PPK. Donald "Red" Grant (Robert Shaw) takes Bond's PPK and holds it on him on the Orient Express. Some Soviet agents also use it, perhaps because Makarov PM's weren't available for the film.
Mauser C96
Grant (Robert Shaw) carries a Mauser C96 with a ten-round magazine, most notably during the gypsy shootout, using it to kill a Bulgarian about to kill Bond.
Walther P38
A Soviet guard at the Russian consulate fires a Walther P38 during Bond's attack, but Bond stops him during a small struggle. (Note: Why a Soviet guard would be carrying a Walther P38 is unexplained)
Guess: Well, they probably couldn't get any actual Soviet pistols since this was made during the Cold War, though I suppose they could have at least given him a Walther PP/PPK, which resembles a Makarov PM.
CZ 45
Grant pulls a Czech CZ 45 .25 calibre pistol from an ankle holster and uses it to intimidate Bond on the Orient Express.
Beretta 418
Rosa Klebb (Lotte Lenya) draws a .25 ACP Beretta 418 pistol with ivory grips during her last-ditch attempt to steal the Lektor from Bond's hotel room. Tatiana Romanova (Daniela Bianchi) uses it to kill Klebb and save Bond.
MP40
The SPECTRE guards on Blofeld's boat carry MP40s, as do the SPECTRE assassins sent to kill Bond via helicopter or boat. Morzeny (Walter Gotell) leads a boat full of MP40-wielding gunmen.
Thompson M1928
One of the SPECTRE trainees is reloading a Thompson M1928 as Klebb and Morzeny walk past. Several others can be seen at a rack in front of training station #1.
Armalite AR-7
Bond uses an Armalite AR-7 survival rifle, issued to him by Q, to assassinate Krilencu. Kerim Bey (Pedro Armendariz) eventually does the shooting. Q mistakenly reports the rifle to be .25 caliber, while it actually fires a .22 Long Rifle cartridge.
Note: It is quite possible that Q has modified a normal Armalite AR-7 to accept .25 ACP cartridges
Armalite AR-10
SPECTRE trainees at the boot camp and rifle range use Armalite AR-10s, among other weapons.
Bren gun
SPECTRE trainees at the boot camp and rifle range also use .303 Bren guns.
Walther LP-53 air pistol
Sean Connery holds a Walther LP-53 air pistol in all promotional shots for the film. It is not a real model firearm, just an air pistol.