Be advised, spoilers are inevitable. Read at your own risk.
Pistols
Glock 17
Seen used by Deputy US Marshals Jimmy Godfrey (Cole Hauser), Luke Watson (Jesse Metcalfe), Marco Martinez (Amaury Nolasco), & Daisy Ogbaa (Rose Rollins). They usually attach SureFire weaponlights when entering tactical situations.
Glock 19
Deputy Marshal Annie Frost (Kelli Giddish) carries a Glock 19 as her sidearm. She usually attaches a SureFire weapon light when entering tactical situations.
Springfield M1911A1
After getting his grandfather's 1911 back, Jimmy started carrying it instead of the standard issue Glock.
Beretta 92FS
Tucker Dawes (Dayo Ade) is seen holding a Beretta 92FS when gun dealers attempt to rob his boss Jack Druggan (Robert Knepper).
Heckler & Koch USP
Lenny Banks is seen holding a USP when gun dealers attempt to rob his boss Jack Druggan (Robert Knepper).
Smith & Wesson 59
Mason Boyle (Travis Fimmel) uses a Smith & Wesson 59 during a home invasion in the pilot episode.
Smith & Wesson Model 36
Jack Druggan (Robert Knepper) uses this compact .38 revolver during his murders in The Comeback Kid.
Smith & Wesson Bodyguard 38
After losing her Glock to Marshal wannabe Bob McGraw (William Lee Scott) Annie retrieves a Smith & Wesson Bodyguard 38 from her bedroom. This is the new polymer framed revolver from S&W.
Used by members of the Marshal team in the pilot episode. Also used by miscellaneous Marshals and other law enforcement personnel. Jack Druggan (Robert Knepper) acquires several M4A1 rifles from some gun dealers, during a shootout with the Marshal team and Houston Police officers he can be seen using a Beta-C drum magazine. Cohorts Tucker Dawes (Dayo Ade) and Lenny Banks are seen wielding them as well.
Colt Model 933
The team makes frequent use of Colt's Model 933 during tactical operations. Jimmy and Marco are seen with them most frequently.
Shotguns
Remington 870 Folding Stock
Annie is seen with a customized 870 folder frequently through the series.
Remington 870
Dallas Police officers can be seen using Remington 870's during the shootout with Jack Druggan (Robert Knepper).
Mossberg 500
Eduardo 'El Lobo' Lopez (Robert LaSardo) is seen using a Mossberg 500 with wood furniture when shooting up Terry Bowden's (Blake Gibbons) trailer home.
Double Barrel Shotgun
While Eduardo 'El Lobo' Lopez (Robert LaSardo) is shooting up his trailer, Terry Bowden (Blake Gibbons) can be seen grabbing a double barrel shotgun from under his couch.
Rifles
Remington 700PSS
A US Marshal sniper is seen providing overwatch for the team when they move on Mason Boyle's (Travis Fimmel) motel room.
Hunting Rifles
When Jimmy took Luke hunting, they both used bolt action rifles. Possibly Remington 700's, but I'm unsure.