In Season 3's "The Leap Home, Part 2" (S3E02), Sam Beckett (Scott Bakula) carries a Stoner 63 configured to be belt-fed as part of his brother Tom's unit in Vietnam.
AKM
Another member of Beckett's unit is armed with an AKM in Season 3's "The Leap Home, Part 2" (S3E02).
AR15/SP1 fitted with M203
Blaster (Patrick Warburton) carries an AR-15/SP1 fitted with the M203 grenade launcher in Season 3's "The Leap Home, Part 2" (S3E02).
CAR-15
Several members of the squad including Tom Beckett carry the CAR-15 in Season 3's "The Leap Home, Part 2" (S3E02). The episode takes place in April of 1970, so the curved 30-round magazines would not be anachronistic.
M134 Minigun
An M134 Minigun is seen mounted in a bunker at the squad's Area of Operations in Season 3's "The Leap Home, Part 2" (S3E02).
M60 machine gun
A Huey doorgunner is briefly seen with an M60 machine gun in Season 3's "The Leap Home, Part 2" (S3E02).
Carcano M91/38
In Season 5's "Lee Harvey Oswald, Part 2" (S5E02), Sam is seen "leaping" into the body of Lee Harvey Oswald and holds the Carcano M91/38, the infamous rifle of the JFK assassination.
M1 Garand
In Season 5's "Lee Harvey Oswald, Part 1" (S5E01), the M1 Garand is used by Sam when he leaps into the body of Lee Harvey Oswald during Marine training.
Ruger Mini 14 GB with folding Stock
In what appears to be a Ruger Mini 14 GB with Folding Stock, a State Trooper arrests Sam Beckett in S5E17 " Revenge of the Evil Leaper - September 16, 1987"