Secret Service Agent Gibbs (Xander Berkeley) uses a Beretta 92FS fitted with a suppressor to execute the Secret Service Agents guarding the armory. Some of the other Secret Service Agents on board Air Force One also use them, even though in real life the Beretta has never been issued to the Secret Service. There is an interesting continuity error in the film, where Agent Walters (Glenn Morshower) (who is trying to evacuate President Marshall via the escape pod) switches from a SIG P226 to a Beretta 92F (see below).
N.B. USSS Agent Gibbs shares the name of the lead character on the TV series NCIS (Mark Harmon). Ironically, the pilot episode of that series takes place aboard Air Force One, investigating a possible terrorist sleeper. A few references to this film are made during the episode.
SIG-Sauer P226
The Secret Service Agents on Air Force One are armed mostly with SIG-Sauer P226 pistols. When the terrorists take over the plane, many of them also use these pistols; Ivan Korshunov carries a P226, which he is commonly seen using to threaten and/or execute hostages. Later in the film, Agent Gibbs is also seen using one.
In real life, the Secret Service would have been using the smaller SIG P228 and P229 at the time of the film's production.
Submachine Guns
Heckler & Koch HK94A3 (mocked-up as MP5A3)
When Secret Service Agent Gibbs (Xander Berkeley) opens up the weapons storage cabinet on Air Force One for Ivan Korshunov's (Gary Oldman's) Russian Ultranationalists, the terrorists get their hands on a number of Heckler & Koch MP5A3 submachine guns. President James Marshall (Harrison Ford) also uses one of these weapons after taking it from one of the terrorists, and both Agent Gibbs and Major Caldwell (William H. Macy) also handle these weapons.
The MP5A3s used in this movie are the same partially-converted HK94A3 carbines from the Stembridge Gun Rentals inventory that have appeared in numerous other motion pictures (including Predator, Lethal Weapon, Die Hard, etc.). Throughout the movie, close-ups of the guns reveal that they have the all-metal 0-1 trigger group of the HK94 (with a "2" position for full-auto engraved), as well as barrels that are missing the attachment lugs (for bayonets, flash hiders, and other accessories). IMFDB's exclusive picture of a "mock MP5" (seen below) is believed to be one of the actual screen-used weapons from Air Force One (though we haven't been able to confirm, since there's no record of the exact serial numbers for all of the weapons that Stembridge sent out to the production).
Heckler & Koch MP5K
A single Heckler & Koch MP5K is among the weapons taken by the terrorists from the weapons cabinet. President Marshall also uses this weapon at one point in the film, and it is also picked up by his wife Grace (Wendy Crewson) while Marshall and Korshunov are fighting. The MP5K used on the plane is a genuine MP5K (or at least, a full-conversion), unlike the terrorists' MP5A3s (which are partially-converted HK94s) and the special forces soldiers' own MP5Ks (which seem to be partially-converted SP89s).
Heckler & Koch SP89 (mocked up as MP5K)
The special forces soldiers who capture General Radek are all armed with suppressed MP5Ks, but they all appear to be partially-converted Heckler & Koch SP89s (or at least, the one used by the team leader definitely is an SP89). Maybe the armorers didn't have access to the MP5K used later in the film when this scene was filmed.
Rifles
Norinco Type 56-1
During the opening scene at the Presidential Palace in Kazakhstan, General Ivan Radek's (Jürgen Prochnow's) military guards are seen using Norinco Type 56-1 assault rifles which have been fitted with AKM-style muzzle breaks (customary for many of the Hollywood Chinese AKs, even though these were not factory-standard). These weapons are also seen in the hands of security officers at Sheremetyevo Airport, which is highly inaccurate.
M4A1 Carbine
The terrorists also take several Colt M4A1 carbine assault rifles from the weapons cabinet, all of which have had their carry handles removed and replaced with C-More optical sights (they also have something attached to the barrel...laser sights?) Ivan Korshunov uses this weapon when the terrorists first start to take control of the plane, firing in vain at the cockpit door at one point. This weapon is also fired by Andrei Kolchak (Elya Baskin). Later in the film, Major Caldwell (William H. Macy) can briefly be seen wielding Korshunov's M4 when President Marshall is running back to the cockpit to call off Radek's release.
Although the fixed-carry handle Colt Model 727 (which is a full-auto version of the earliest M4, AKA the Model 777) had already appeared in Crimson Tide and Broken Arrow when this movie came out, it appears that Air Force One is the very first Hollywood film to feature the flattop M4 carbine that is so familiar to American audiences today.
M727 with M203 grenade launcher
A Colt Model 727 carbine with an M203 grenade launcher is carried by one of the Air Force rescue team officers who is sent to retrieve President Marshall's escape pod (lack of detachable carry handle means it's not an M4).
Custom Short-barreled AKMS
During the scene where General Radek is about to be released from prison, several of his troops land at the front gate in an Mi-24 Hind helicopter gunship and then line up to greet him. All of them are using an AK variation of unknown make and model. They look similar to the short-barreled AK used by Art Malik in True Lies, which is almost certainly not a coincidence because Harry Lu was the armorer on both movies; the only difference is that the guns have been fitted with side-folding stocks for Air Force One (which appear to have been borrowed from Hungarian AMD-65s).
AKM
The guards at the Russian prison fire at General Radek as he flees with AKM rifles, which may be correct because prison guards are considered rear echelon troops.