XM177-type carbines are the main weapons carried by LT Jordan O'Neill (Demi Moore) and the majority of the applicants in the SEAL CRT program. During the Libyan mission, the weapon is carried by Master Chief Urgayle (Viggo Mortensen) and other members of the team. The XM177s in the movie all have M16A2 or Model 715-style receivers, while the real XM177 variants only had M16A1 or SP1-type receivers. Rifles similar to these have appeared in many other movies and TV shows, such as The Rock and Seven Days.
In one scene, a weapons instructor describes the gun as a "CAR-15, military designation M4", but the guns shown in the movie are quite clearly not M4s.
An M203 Grenade Launcher is seen attached underneath O'Neill's XM177 during the Libyan mission as well as carried by the SEAL applicants during the obstacle course.
The M60E3 is seen being assembled by O'Neill and other members of her team during the SEAL training. It is also the chief weapon of Cortez (David Vadim) during the Libyan mission.
A DShK is seen mounted on a Libyan truck that fires on the team. It's hard to tell, but this is most likely a mocked-up Browning M2 variant, like nearly all "DShK" HMGs seen in Western productions.
Master Chief Urgayle (Viggo Mortensen) uses a Heckler & Koch SR9(T) during the Libyan mission. The SR9(T) in this movie, like all SR9 rifles seen in American films, is actually a HK91 converted to SR9(T) specifications (note that it lacks the forward assist, which is a feature of the factory SR9 variants). While being chased by Libyan soldiers, he booby traps the weapon with a M67 grenade.