The Beretta 92FS is by far the most commonly-seen gun on the show, used by Jericho police, military personnel, agents, and various other characters. Nearly all of the show's characters, including Jake Green (Skeet Ulrich), Jake's father Johnston Green (Gerald McRaney) and brother Eric Green (Kenneth Mitchell), Stanley Richmond (Brad Beyer), and Robert Hawkins (Lennie James) have used the 92FS in more than one episode. Hawkins in particular uses 92FS' in nearly every episode, including at least one with a suppressor.
Beretta Mini Cougar 8000 F
Robert Hawkins (Lennie James) is seen in several episodes using a Beretta Mini Cougar 8000 F with an Inox finish, in keeping with his apparent preference for Berettas (he also uses the 92FS regularly, as mentioned above). This is also the gun he teaches his daughter Allison (Jazz Raycole) to fire in Episode 1.6, "9:02". Hawkins' wife Darcy (April Parker-Jones) also uses this gun in some episodes.
Glock 19
The Glock 19 is another gun that is used by many characters throughout the show, including Eric Green (Kenneth Mitchell) in several episodes. This gun is also used by Jake in Episode 1.15 to shoot at the bandits from a moving truck. After the truck crashes, he tries in vain to reach the gun. A mercenary stalking Hawkins and Sarah in the same episode is also seen brandishing one.
Ruger KP89
In several episodes of Season 1, Jake Green uses aRuger KP89 pistol. It is seen most prominently in "A.K.A." (S1E19), when Jake confronts Hawkins over the possibility that he might be a terrorist. Jake uses this gun again in "Casus Belli" (S1E20), but he loses it when he is captured by Sheriff Constantino (Timothy Omundson) and his men in New Bern's munitions factory.
SIG-Sauer P226
Jake also uses a SIG-Sauer P226 in Episode 1.22, "Coalition of the Willing", when he hijacks the New Bern truck carrying mortar rounds. He is never seen using it again after this episode.
Kimber Warrior
A Kimber Warrior 1911 is given to Eric by the scared Ravenwood mercenary when they are at Rogue River and trying to distract the other mercenaries so that they can grab medicine from the hospital. Eric never gets a chance to use it, though.
Revolvers
Colt Python
A Colt Python is used by Jake Green (Skeet Ulrich) in Episode 1.2, "Fallout", and later wielded by a police officer in the next episode. He uses it again in several other episodes throughout the first season.
Colt Single Action Army
A .45 Colt Single Action Army (or, likely, an Uberti replica) is wielded by Emily Sullivan (Ashley Scott) in "Fallout" (S1E02), and used to kill one of the convicts posing as a police officer.
In "One Man's Terrorist", Gray Anderson (Michael Gaston) and Roger Hammond (Christopher Wiehl) get into an argument over refugees, which leads to Gray pulling a Smith & Wesson Model 27 with a 4" barrel on Roger. Roger gets the gun away from him, shoots him in the stomach, and later holds Jake, Emily, and Gray hostage in Gray's office with the gun until a deal is made for the refugees to stay.
Submachine Guns
Heckler & Koch MP5K-PDW
Hawkins and Sarah use Heckler & Koch MP5K-PDWs with C-More sights atop claw mounts when they storm the house of the "old man" in Episode 1.15, "Heart of Winter". Hilariously, Hawkins' MP5K has its charging handle locked back throughout the episode, rendering it useless should he need to fire it (though he never does). Also seen, briefly, in the hands of a New Bern gunman during the attacks on the mortar sites.
Heckler & Koch UMP
Though not really clearly seen, it appears that in "Why We Fight" (S1E22), a Marine radio operator from the Allied States of America (judging by the flag on his shoulder) is armed with the Heckler & Koch UMP (this conclusion is basically drawn from the shape of the stock seen against his chest).
MAC-10
Used primarily by Jonah Prowse's gang in the series is the MAC-10 machine pistol.
IMI Uzi
Another weapon seemingly only used by Prowse's gang is the Israeli classic Uzi SMG.
Sniper Rifles
Barrett M82
A Barrett M82 is briefly seen carried by a trooper riding on a deuce and a half in "Why We Fight".
In several episodes, Hawkins is seen using a Remington 700 AICS sniper rifle, fitted with a Harris bipod. In the episode "Crossroads", it has a suppressor and laser sight (the latter of which is highly inappropriate for a sniper rifle, but was successful in its job to intimidate Goetz into leaving).
Winchester Model 70
Winchester Model 70 rifle appear in several episodes in the hands of townsfolk. Hawkins uses one in Episode 1.9, "Crossroads".
Rifles
M1 Carbine
M1 Carbines appear in many episodes in the hands of Jericho townsfolk. Jake can be seen using one in Episode 1.11, "Vox Populi".
M14 Rifle
Seen, though never actually used in combat, is the M16's immediate predecessor the M14 Rifle. The weapons themselves are either Springfield M1As or the Norinco M14S. One is used in combat by Hawkins when they captured Geotz.
Colt M16A2
When Jericho and New Bern go to war, both sides make heavy use of the Colt M16A2 assault rifle. Hawkins distributes a large cache of these weapons to the citizens of the town, and they are used by Jake, Eric, Stanley, Johnston, and many other important characters.
Colt M16A4
The Colt M16A4 is also used in many episodes, mostly by Major Beck's soldiers, though also by some of Jericho's townsfolk in the war with New Bern. Due to a continuity error in the opening of Episode 1.23, "Why We Fight", Eric goes from using an M16A2 to using an M16A4.
M4A1 Carbine
Colt M4A1 carbines are used very often in the show. They are first seen being wielded by the Ravenwood mercenaries in "Rogue River" (S1E8). Hawkins is also seen unloading a crate full of them in "Four Horsemen" (S1E3). The fake Marine sergeant in "Semper Fidelis" (S1E16) is armed with an M4 that becomes an HK416 in a continuity error.
Heckler & Koch HK416
In a continuity error, the fake Marine sergeant's M4 is replaced by a Heckler & Koch HK416 is used by one of the fake Marines in "Semper Fidelis" (S1E16).
Heckler & Koch G36C
Seen only once in the hands of Stanley Richmond, though never fired, is the Heckler & Koch G36C.
AKM
Used by citizens of Jericho and New Bern in several episodes are many AKM assault rifles. Hawkins uses one in Episode 1.22, "Coalition of the Willing".
L85A1
A possible L85A1 was sighted at the end of "Coalition of the Willing" (S1E21) in the hands of one of the rangers. It was extremely hard to tell and to screen cap because of the movements and because it was a night scene.
Shotguns
Ithaca 37
Ithaca 37 shotguns can be seen in a number of episodes. Jake and Eric use the riot model when they go to Rogue River's hospital in "Rogue River" (S1E8).
Mossberg 500
Mossberg 500 smooth bore duck gun with raised barrel ribbing. Could also be 835 but I'm pretty sure it is just a 500.
A Benelli M3 Super 90 is used by a Jericho citizen when Ravenwood tries to enter the town in Episode 1.9 "Crossroads"
Machine Guns
Browning M2HB
A Browning M2HB is seen on the fake M1 Abrams (actually a visually modified British Chieftain tank, also seen in Jarhead) in Episode 1.16, "Semper Fidelis". Also seen mounted on a flatbed guard post to New Bern in "One If By Land".
FN M249E2
Seen only briefly in "Semper Fidelis" in the hands of a Marine and and the season 1 finale "Why We Fight" is this successful Belgian design which is, given the heat shield and synthetic stock, the M249E2.
M60 machine gun
Used by the attacking citizens of New Bern during their firefight with Jericho in "Why We Fight" is the M60 machine gun.
M240
A pintle-mounted M240 is also seen on the Abrams in Episode 1.16.
Other
M203 grenade launcher
One of the fake Marines in "Semper Fidelis" is armed with an M16A2 fitted with an M203 grenade launcher.
Hawkins' Locker Arsenal
Seen on a wall mounted rack in Hawkins' storage locker arsenal in "Coalition of the Willing" are 18 different handguns which appear to be all semi-autos of different calibers.