Axel Foley's (Eddie Murphy) sidearm in this movie is a Browning Hi-Power pistol. The manufacturer, FN, switched from an internal extractor to the external extractor in the early 1960's. This help date Foley's gun as a post-WWII pistol. Axel uses a Hi-Power in all the other movies in the series.
IMI Uzi
Maitland's thug use IMI Uzis during the final gunfight at the end of the film.
A police officer at the beginning of the film uses a Smith & Wesson Model 639 as his sidearm. Detective Jeffrey Friedman (Paul Reiser) can be also seen with one tucked in his waistband. One of Maitland's thugs also uses one to hold Axel and gunpoint, and later to shoot at Billy Rosewood. Lt. Bogomil (Ronny Cox) uses this as his primary sidearm, as seen during the climax of the film. It is likely that the same gun was used in all scenes because they all have wood grips and adjustable sights.
Dan Wesson revolver
One of the Beverly Hills PD officers uses a 4" barreled revolver with enclosed ejector rod and ventilated rib. At first sight it looks like a Colt Trooper, but looking closely, it can be identified as a Dan Wesson revolver.
Note that the cylinder opening latch is located ahead of the cylinder, a feature only found in Dan Wesson revolvers (arrow)
Ithaca Shotgun
A Ithaca shotgun is used by one of the strip club robbers and John Taggart (John Ashton).
Double barreled shotgun (unknown brand)
Used by the other strip club holdup men
Unidentified firearms
We can see several handguns that are hard to identify precisely:
In the opening scenes, we can see several revolvers with fixed and adjustable sights, used by the Detroit PD officers. They are probably S&W model 10 & 19
Another officer in this scene uses an auto pistol (S&W?)
Gilber R. Hill, in his role of Inspector Todd, carries an auto pistol inside the waistband. It doesn't seem to be the S&W 639 seen in other scenes (I think that this pistol has fixed sights)
It could be a Colt MK IV series 70, the grips definitely look like Colt grips.