Starting with "Little Green Men" (S2E01), Fox Mulder (David Duchovny) used a SIG-Sauer P226. Following this episode, Mulder carried the P226 for the entirety of the show, with the exception of Season 3, when he and Scully both used Smith & Wesson 5906s.
SIG-Sauer P225
There were several episodes, mostly in Season 5, where Scully used a SIG-Sauer P225 rather than the P228 she used normally. This might have occurred because the show's armorer was unable to bring a P228 on-set for those particular episodes. Scully used the P225 from "Unruhe" (S4E02) until "The End" (S5E20).
Makarov PM
In the episode "Terma" (S4E09), a number of Russian guards on horseback are seen armed with Makarov PM handguns as they shoot at Mulder while he is escaping the Tunguska gulag during "Terma" (S4E09).
Smith & Wesson 5906
Dana Scully uses the Smith & Wesson 5906 handgun that she used in Season 3 in the Season 4 premier episode "Herrenvolk" (S4E01).
NOTE: Several users have suggested that these pistols might be the Smith & Wesson 1076 in 10mm, which was briefly used by the FBI. This is incorrect; the 1076 has a single-stack frame, while the pistols in the show have double-stack frames, meaning that they can only be the model S&W 5906. The show's guns are not the .40-caliber model 4006, because the 4006's frame features checkering on the grip, missing on the show's Smith & Wessons (the 5906 frame has vertical grooves on the grip). The model S&W 1076 can be easily distinguished from the S&W 5906, as the 1076 is hammerless, has no manual safety and a frame mounted de-cocking lever. This is a TV show, not real life, and movie/television armorers have always tended to use 9mm pistols rather than larger calibers, because 9mm blanks are more reliable to cycle in pistols than larger calibers.
Ruger KP89
'Deep Throat' (Jerry Hardin) uses a Ruger KP89 to shoot an alien in "Musings of a Cigarette-Smoking Man" (S4E07).
Unknown pistol
During "Tunguska" (S4E09), Alex Krycek (Nicholas Lea) tosses an unknown pistol out of the window of a truck when he surrenders to Mulder.
Revolvers
Oswald's revolver
Lee Harvey Oswald uses a revolver to shoot a policeman during episode "Musings of a Cigarette-Smoking Man" (S4E07).
Mulder's revolver
In a dream during "Paper Hearts" (S4E10), Fox Mulder grabs a revolver from a box. This is the same revolver he attempted to use to save his sister Samantha from alien abduction as a child.
Unknown police revolvers
During "Musings of a Cigarette-Smoking Man" (S4E07), the police who attempt to Lee Harvey Oswald are armed with various revolvers. None are seen very clearly.
Rifles
M16A1 rifle
The M16A1 rifle was used on a regular basis throughout The X-Files run as either a military and/or SWAT weapon. M16A1 rifles are used by the militia gunmen and several FBI agents in the episode "Tunguska" ((S4E08).
M14 rifle
Used by a militia gunman in the episode "Tunguska" ((S4E08).
Norinco Type 84S
The Norinco Type 84S is seen used by guards at the Tunguska gulag in the episode "Terma" ((S4E09).
The Cigarette-Smoking Man's Rifles
The Cigarette-Smoking Man uses three rifles during "Musings of a Cigarette-Smoking Man" (S4E07).
Dana Scully (Gillian Anderson) uses an MP5A3 with an attached flashlight during the FBI raid on the militia in "Tunguska" (S4E08)
Shotguns
Fox Mulder's shotgun
Fox Mulder (David Duchovny) uses an unkown shotgun with a pistol grip and mounted flashlight during the FBI raid on the militia group in "Tunguska" (S4E08).