James Bond (Timothy Dalton) carries his usual Walther PPK as his weapon of choice throughout the film. However, this particular PPK is a WWII-era German Waffenamt variant (it should be noted that the PPK used in Licence To Kill was sourced from Stembridge Gun Rentals instead of Bapty and Co. since the movie was filmed entirely in the US and Mexico). This is most likely the same PPK Dalton had carried in the previous film, The Living Daylights.
Taurus PT92
During the pre-credits sequence, CIA Agent Felix Leiter (David Hedison), gives James Bond (Timothy Dalton) a Taurus PT92 "just in case". Bond uses it during the shootout against the henchmen that attack him, Leiter, and his fellow DEA Agents, using it moments later to shoot the Jeep's left front tire. Milton Krest (Anthony Zerbe) uses a PT92 to shoot at Bond on Krest's boat when he kills a diver and jumps off. The film's armorer states clearly its a Taurus PT92 and not a Beretta 92FS.
Heckler & Koch P9S
Braun is armed with a Heckler & Koch P9S. He is later seen carrying it on the Wave Krest.
When Bond hijacks the seaplane full of money, one of the pilots pulls a Smith & Wesson Model 15 on Bond and attempts to shoot him with it (instead shooting a package of money), but Bond knocks it out of the pilot's hand.
Smith & Wesson Model 66
Dario (Benicio del Toro) grabs a Smith & Wesson Model 66 from one of his henchmen in the bar and uses it to fire at Bond and Pam as they get away on the boat.
Beretta 950 Jetfire
Pam (Carey Lowell) carries a stainless steel Beretta 950 Jetfire as her sidearm throughout the film, giving one to Bond, and grabbing a spare one out of her purse when Bond leaves to check the hotel room. She also notably uses her Bobcat when she meets Professor Joe Butcher (Wayne Newton) when she goes to "study" with him.
During the tour of Sanchez' drug lab, Dario (Benicio del Toro) pulls a Walther P5 on Bond. This was the same pistol issued to Bond when he'd "mislaid" his PPK in Octopussy.
Unknown pistol/revolver
When Bond made his escape, one of the MI6 agents tried to shoot him with this weapon, but was stopped by M.
Unknown Smith & Wesson revolver
Seen in the holsters of Florida Keys police officers.
Submachine Guns
Heckler & Koch HK94A3 (Chopped and Converted)
Many of Sanchez's henchmen are armed with H&K HK94A3s chopped and converted to look and act like MP5A3 submachine guns. Dario (Benicio del Toro) carries one on the Jeep in the pre-credits sequence. The guard (Carl Ciarfalio) at Milton Krest's warehouse carries one, as do several of Sanchez's men during the final car chase. The Majority of the film was made in both the US and Mexico and the production crew sourced their weapons from Stembridge Gun Rentals instead of Bapty and Co (the traditional armorers for the James Bond movies).
Micro Uzi
One of Sanchez' henchmen and Sanchez (Robert Davi) himself use Micro Uzis.Interestingly, in the truck chase, if you listen to the bullet impacts, they plink out some phrases from the James Bond theme song. Sanchez also notably killed Truman Lodge with this weapon after he sarcastically congratulated him with an "80 million write-off" (Bond destroyed most of Sanchez's cocaine gasoline blend shipment during the final car chase).
The DEA agents and soldiers that escort the prison van carrying Sanchez and the soldiers in the fictional country of Isthmus use M16A1 rifles fitted with M16A2 handguards.
Shotguns
Remington 870
Ed Killifer (Everett McGill), the DEA agent that Sanchez bribed to get him out of custody, carries a Remington 870 shotgun in the prison van, using it to knock the driver out and take control of the van and run it off a bridge. They were also seen carried by Bank of Isthmus City security guards during the scene that introduces Truman Lodge.
Mossberg 500 Cruiser
CIA Agent Pam Bouvier (Carey Lowell) uses a sawed-off Mossberg 500 Cruiser during the bar fight. It blows a hole in the wall somehow big enough for a human to fit through.
Launchers
FIM-92A Stinger
During the final car chase, Perez, one of Sanchez's henchmen, attempts to use an FIM-92A Stinger to try and kill Bond, but Bond dodges the missile by tilting his tanker on its left side wheels, making the missile miss and hit another tanker behind him. Sanchez later attempts to use one to take down Pam's plane when she flies low over the tanker Sanchez is on, but the missile goes through the tail. It is incorrectly portrayed as a conventional rocket launcher.
Other
Spear Gun
Used by Bond and Krest's men during a scene at the Florida Keys.
Unknown Sniper Rifle
Used by an MI6 agent who is standing on the lighthouse at Hemingway House to shoot at a Bond as he made his escape.
"Signature Camera Gun"
Q makes Bond a customized Camera Gun to assassinate Sanchez, which can only be fired by him (explaining why the Chinese Intelligence agents cannot get it to work). Q identified the gun's "film" as .220 high-velocity.