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.
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.
Mauser Kar98k
Mauser Kar98k rifles were seen in the hands of SPECTRE guards at SPECTRE island. Mauser Kar98k rifles were also seen in the hands of both the Gypsies and the Bulgarian agents later in the film.
This Sten Mk.V can also be spotted at the firing range.
Bren gun
SPECTRE trainees at the boot camp and rifle range also use .303 Bren guns.
Flamethrower
One of the SPECTRE trainees at the boot camp is also seen with a flamethrower.
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.
Llama XVIII Especial
Grant pulls a Spanish Llama XVIII Especial .25 calibre pistol from an ankle holster and uses it to intimidate Bond on the Orient Express. Rosa Klebb (Lotte Lenya) draws a .25 ACP Llama XVIII pistol with pearl grips during her last-ditch attempt to steal the Lektor from Bond's hotel room.
Beretta 418
Tatiana Romanova (Daniela Bianchi) picks up Rosa Klebb's dropped gun that has become a .25 ACP Beretta 418 pistol with pearl grips, and uses it to kill Klebb and save Bond.
Trivia: In the early novels, James Bond's sidearm was a Beretta 418. In the novel "From Russia with Love", it gets caught in Bond's holster, which nearly costs him his life. In the following novel, "Doctor No", M forces Bond to switch to a new weapon: the Walther PPK.'
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.
SPECTRE agents use what appear to be mocked-up or dummy Energa rifle grenades (designated by the British as Grenade, Rifle, A tk, No. 94 Mk. 1, and by the US Military as M28) attached to Lee-Enfield No.4 rifles.
Gun Barrel opening sequence
Again, as in the Dr. No we can see Bond shooting his Walther PPK at someone holding Smith and Wesson revolver, in the barrel of which camera's pretending to be. And again, it's not Sean Connery, it's Bob Simmons, who we seen in this scene.
It's need to be noted, that sequence is not 100% identical to the one in Dr. No.