Bob (Tracey Walter) uses a Colt M1911A1 throughout the movie on several occasions. A random goon also uses one later in the movie.
Colt New Service
Jack Napier/The Joker (Jack Nicholson) uses a Colt New Service throughout most of the film including the BANG flag gun at the film's climax. The only exception is one small edit when he pulls back the hammer is the Axis Chemical plant. A different pistol was used for this one shot.
The Joker (Jack Nicholson) uses a Smith & Wesson Model 1 when he confronts Bruce Wayne. A metal plate Bruce hid under his shirt stops the bullet.
Unknown Revolvers
There are a great many revolvers used in this movie, I will just post all revolver screens in this section, as I am no good at identifying them. Maybe someone else can.
I see Model 19s, Colt New Services, and Webleys. Maybe even more. - Gunmaster45
Hey there, decided the Batman page needed building, I'll try to split up the revolver section when I get more info, thanks for your help. - Diego Wolfwood
M1928 Thompson
The Joker's goons use M1928 Thompson Submachine Guns multiple times throughout the movie.
Unknown Double Barrel Shotgun/Flare Gun
The Joker uses this weapon to shoot his TV, then proceeds to hand it to Bob.
Browning M1919
The guns that pop out of the Batmobile's fenders are two Browning M1919's. Seen toward the end of the movie as the Batmobile is entering the chemical plant.
GE M134 Minigun
Batman has a GE M134 Minigun equipped on the Batwing, and uses it to shoot at The Joker near the end of the movie.