Major Misato Katsuragi's gun is the HK USP. Unlike most Nerv personnel, she does not use the standard issue Glock 17, possibly because she is head of the Tactical division. She brandishes it several times during the series. Note that Misato's USP has a rubber grip on the handle. She fires 10 rounds in succession when fighting the JSSDF soldiers. All three of the main H&K USP variants carry more than 10 rounds per magazine, so there is no on-screen evidence establishing which kind she uses (According to Evangelion Chronicle #13, her USP is a .45 ACP variant).
The Inglis Hi-Power is the standard-issue sidearm used by Japanese Strategic Self-Defense Force commandos. It can be identified as such by its distinctive rear sight.
According to Evangelion Chronicle #22, Aoba's personal submachine gun is a hybrid consisting of parts from a Steyr MPi 69 and the Russian AEK-919K Kashtan. While normally only Nerv security guards are armed with submachine guns and normal technicians and computer operators are only armed with Glock 17s, command center computer operator Lt. Aoba either manages to get his hands on one or kept one stored in his desk for just such an eventuality.
The advanced Heckler & Koch G11 is the standard weapon of the elite JSSDF commandos who invade Nerv HQ in End of Evangelion. The G11's caseless ammunition is accurately depicted, as the JSSDF's G11s never eject casings (as opposed to their Hi-Powers, which do); its reciprocating magazine, on the other hand, is not.
The MAS NF-1, which is a variant of the AA-52 machine gun mounted on French-made military vehicles, is seen mounted in a co-axial position on JSSDF AMX-10RCs as they lay a bombardment on Nerv HQ in the beginning of End of Evangelion.
United Nations Army and JSSDF Mitsubishi Type 74 MBTs are armed with the Sumitomo M2, the licensed-made version of the Browning M2 as the secondary weapon.
M269 Modules mounted on UN Army-controlled MLRS are used to fire M26 rockets at Sachiel when it begins to approach Tokyo-3 in the first episode. JSSDF-maned MLRS use them in End of Evangelion when they take on Asuka's Unit 02.
The Evangelions (or simply Evas), the massive humanoid constructs around which much of the story's plot centers, use a variety of weapons; while some are fictional, many are based off of real-world firearms (albeit visually modified, and scaled up to fit the Evas' massive size).
Steyr ACR
The most prominently-featured weapon used by the Evas is a scaled-up Steyr ACR, referred to for unclear reasons as a "Pallet Rifle". It is never shown being reloaded (the Evas simply dropping them when they run out of ammunition), nor is it ever shown ejecting spent casings (implying that, unlike the real ACR, the Pallet Rifles use caseless ammunition of some form); it apparently fires explosive shells, and is shown as being more or less useless in every one of its appearances barring Episode 11.
A major plot device of Episode 9 is the "Positron Rifle", a prototype energy weapon under development by the JSSDF; it is "requisitioned" by Nerv and rebuilt for Eva use, with the resultant weapon seemingly based on the PTRS-41 anti-tank rifle. Notably, it features a series of cables attached to it (most prominently to a large block where the PTRS's magazine would be); these are plugged into the weapon's power source, which consists of the entire Japanese national grid. The weapon is also used in Episode 22, albeit to considerably lesser effect, and apparently without its national-blackout requirement.
Error creating thumbnail: File missingPTRS-41 - 14.5x114mmError creating thumbnail: File missingThe initial establishing shot of the Positron Rifle, as seen from above; note the distinctive muzzle brake and offset front sight (though what an energy weapon with a computerized optical sighting system needs either of those things for is unclear).Error creating thumbnail: File missingBeing as long as it is, the Positron Rifle rarely fits on screen; as such, the only good full-profile shots of it to be had are stitched-together images like this one. While it may appear to be bent, this is simply a result of the shifting perspective of such a shot.Error creating thumbnail: File missingUnit-01 racks the weapon's charging handle, immediately after an order is given to "clear the chamber".Error creating thumbnail: File missingIt's not clear whether or not these two events are linked, since the actual apparent purpose of doing this is to load in one of the rifle's massive fuse units. These are presumably impossible to fire the rifle without, given that the pop-up "DANGER" indicator behind the "bolt" only pops up once one is chambered.Error creating thumbnail: File missingAnother stitched image; apparently, much of the rifle is purple. Also note the large tube above the barrel labeled "FX-1"; on the original PTRS, this is a gas tube. It's not entirely clear how this tube manages to stay straight, seeing as it's only attached to the rifle's receiver and another power cable.Error creating thumbnail: File missingThe Positron Rifle fires in two stages; first, the large, eight-holed block attached to the right side of the receiver is hit with eight white beams.Error creating thumbnail: File missingThen, the rifle actually fires, with enough muzzle blast to push all the nearby trees around.Error creating thumbnail: File missingA shot of the rifle's muzzle brake, right as an attack from Ramiel lands behind Unit-01; note how the front sight now extends straight up instead of at an angle.Error creating thumbnail: File missingUnit-01 readies another shot; note that the wires in the old fuse unit (the one being ejected) are severed.Error creating thumbnail: File missingThe Positron Rifle's targeting system; despite all the importance given to correcting for variation by Dr. Akagi, the only thing the pilot apparently has to do is wait for the two symbols to align in the center.Error creating thumbnail: File missingOnce they do so, the reticle changes into this.Error creating thumbnail: File missingA good view of the muzzle brake as Unit-01 fires its second shot; note that only two of the brake's several ports are actually used.
IMI Desert Eagle Mark XIX
In Episode 16, Shinji's Eva Unit-01 is seen using a handgun which appears to be a scaled-up, but otherwise completely unaltered IMI Desert Eagle Mark XIX, right down to the rather baffling inclusion of the scope mounting rails; it is used to little effect against the episode's Angel, and is never seen again (presumably having been lost in the Dirac Sea said Angel created).
Rei's Eva Unit-00 is seen on two occasions (Episodes 16 and 23) with a sniper rifle based on the Accuracy International Arctic Warfare; alongside alterations to the profile of the stock, the most prominent difference between the real rifle and the Eva version is that the latter is semi-automatic.
Asuka's Eva Unit-02 is seen with an unidentified, possibly-fictional repeating rocket launcher on two occasions (Episodes 18 and 19). In the former, she doesn't ever fire the weapon, while in the latter she dual-wields them; for entirely unclear reasons, this does practically nothing to her target.