Because Mars Attacks! is meant to spoof alien invasion flicks from the 1950s and 60s, the United States Army in the film uses equipment and uniforms that were in use during that time period, in keeping with the production aesthetic. Consequently, all soldiers in the film carry the M14 battle rifle in 7.62x51mm NATO, which had long since been replaced by the M16 rifle family at the time of the movie. During the first encounter with the Martians, Billy Glenn Norris (Jack Black) grabs a discarded M14 and tries to shoot the Martians with it, only to learn it is empty (which causes the magazine to fall out for some reason).
It is interesting to note that very few of the M14s in the film seem to fire blanks; it is often possible to see that the muzzle flashes of some rifles were added in post-production, that the actions do not cycle to eject blank casings, and that the actors playing the soldiers are faking the recoil. Also, the rifle that Billy Glenn Norris field-strips and then re-assembles in his trailer clearly has no selector, which means it is most likely a commercial semi-automatic M14 clone (such as a Springfield Armory M1A or a Norinco M14S).
Handguns
M1911A1
General Decker (Rod Steiger) welds a pair of M1911A1 pistols akimbo whilst shouting at the Martian leader, which do no harm to the Martians as he's shrunk while firing them and then crushed underfoot. An interesting goof is that while he's firing at the Martians, one of his 1911s clearly goes empty, yet gunshots are still heard, and after a split-second cut to the Martians (with no time to reload), he is shown firing both guns again as though nothing happened. It is also interesting to note that during the White House attack, the Martian airhelmets can be cracked by a Beretta's 9mm bullets, but for some reason, General Decker's .45s are not strong enough to break the airhelmets.
Beretta 92FS
The Secret Service Agents in the movie all carry Beretta 92FS pistols (even though in real life, the SIG-Sauer P228 would have been standard-issue to the USSS at the time of the movie).
Colt Official Police
While in his trailer, Mr. Norris (Joe Don Baker) loads a revolver which isn't seen clearly, but appears to be a short-barreled Colt Official Police with a 4" barrel (judging by the shape of the hammer and the half-moon shaped front sight).
Machine Guns
Browning M2HB
Browning M2HB heavy machine guns can be seen mounted on U.S. Army tanks and jeeps (note that the tanks in the film are also old-fashioned M-41s). When the Martians fry Congress, General Decker (Rod Steiger) gets on a tank and fires one at the Martian space ship. As with most of the film's M14s, the M2HB does not seem to be firing blank ammunition; it ejects no shell casings and the muzzle flash was clearly inserted in post-production.
Browning M1919
The Browning M1919 machine guns are seen mounted on several jeeps during the welcome event in the Nevada desert. The machine guns are also mounted on APCs when soldiers battle the Martians in Las Vegas.
Submachine Guns
Micro Uzi
Mitch (Brian Haley), the main Secret Service agent guarding President James Dale (Jack Nicholson), pulls a Micro Uzi and then fires at the attacking Martians who enter the War Room.
Shotguns
12 Gauge Double Barreled Shotgun
Sue Ann Norris (O-Lan Jones) and Mr. Norris (Joe Don Baker) load shotguns when preparing to fight the invading Martians, though they don't get a chance to use them as a Martian robot smashes their trailer with them inside. The one used by Mr. Norris has a 12 Gauge double barreled shotgun with two exposed hammers, so it's definitely an older-style design.
Mr. Norris throws Richie Norris (Lukas Haas) a shotgun and tells him to "lock and load", but Richie drops it to go and get his grandmother, Florence Norris (Sylvia Sidney). The shotgun appears to be a Winchester Model 1912, judging by the shape of the pump when Richie catches it.