A Blastech IB-94 blaster pistol is used by the Mandalorian aka Din Djarin (Pedro Pascal) as his main sidearm. It is based on the Bergmann 1894; because of the rarity of the real pistol, it seems likely that the prop used in the show is a replica instead of an actual Bergmann 1894. A number of modifications were made to the Bergmann 1894 for the blaster's design, including new iron sights, a muzzle device, a modified grip, a modified hammer, and a smoothed out magazine cover with the circular grasping handle removed. The blaster's designation, IB-94 (resembling "1894"), is a clear reference to the pistol it's based on.
WESTAR-35 Blaster Pistol (STI Perfect 10)
In "Chapter 3: The Sin", several Mandalorians use WESTAR-35 Blaster Pistols in the shootout with the Bounty Guild. These pistols appear to be based on STI Perfect 10s fitted with a cosmetic shell that covers the entire slide and the front of the frame. Several of the Fighting Corp Mandalorians from "Chapter 8: Redeption" also seen with the WESTAR-35 blaster pistol, either in use or holstered.
BlasTech DH-17 Blaster Pistol (C1 Submachine Gun)
The BlasTech DH-17 Blaster Pistol, based on the Sterling SMG, is used by some Mandalorians backing up the Mandalorian at the end of "Chapter 3: The Sin". In "Chapter 6: The Prisoner", New Republic Security Droids use the DH-17 as their primary weapon, then the Mandalorian uses it to bust of a jail cell.
BlasTech SE-14R Blaster Pistol (Rexim-Favor Mk5)
The Rexim-Favor Mk5-based "BlasTech SE-14R" is used by Remnant Stormtroopers as their sidearm. Then in "Chapter 8: The Redemption", the Death Troopers also carry the SE-14R as their sidearm, but don't use them.
Ruger Mk II
A suppressed Ruger Mk II is seen with a Rodian-type Guild bounty hunter in "Chapter 3: The Sin".
Rodian DT-12 (Ruger Mk III)
Migs Mayfeld (Bill Burr) is seen using the "Rodian DT-12" blaster pistol, a heavily-modified Ruger Mk III in "Chapter 6: The Prisoner". Quin then breifly uses one of Mayfeld's DT-12s after The Mandalorian takes control on the ship.
A highly modified Astra 400 appears in the Mandalorian's Arsenal, and is later one of the weapons used to arm the farmers in "Chapter 4: Sanctuary". An identical pistol is also carried by one of the guild bounty hunter in "Chapter 3: The Sin". Mayfeld (Bill Burr) is also seen using the same model in "Chapter 6: The Prisoner".
Accles & Shelvoke Acvoke
An Accles & Shelvoke Acvoke air pistol fitted with wooden grips and a reversed M38 azimuth telescope on the right side can be seen in the Mandalorian's arsenal. This is also one of the weapons which he uses to arm farmers with in "Chapter 4: Sanctuary".
Apache Fireball Air Pistol
An Apache Fireball Air Pistol fitted with a ribbed barrel shroud is in the Mandalorian's arsenal, and is also one of the weapons he uses to arm the farmers in "Chapter 4: Sanctuary".
Webley Tempest Air Pistol
A Webley Tempest Air Pistol modified with a wider and longer barrel appears in the Mandalorian's arsenal. It is also used by at least one of the guild bounty hunters in "Chapter 3: The Sin". Toro Calican (Jake Cannavale) carries this pistol fitted with a scope (the same M38 azimuth telescope seen on many Star Wars weapons) and a cone shaped muzzle device in "Chapter 5: The Gunslinger".
Webley Premier Air Pistol
A heavily modified Webley Premier Air Pistol is used by Mayfeld (Bill Burr) in "Chapter 6: The Prisoner". The pistol has had the original barrel entirely removed and instead the piston tube portrays the barrel and is fitted with a cone shaped muzzle. A block has been fitted ahead of the rear sight to hide the original now empty breech area, and what appears to be an aiming laser is fitted above the muzzle. Based on the number of trigger pins and the rounded washer-like sections at the bottom of the barrel locking latch, this appears to be a Model E variant of the pistol.
A180 Pistol (WE Luger P08)
Davan (Matt Lanter) uses an A180 pistol, which was based on a Luger P08 in "Chapter 6: The Prisoner". This pistol first appeared in Rogue One: A Star Wars Story and is built from the same model WE Luger P08 6" barrel airsoft pistol, however it is a different physical prop as this example retains the original intact rear sight and has not had the over-travel lug on the rear of the toggle ground down.
Karga's Blaster Pistols (Steyr M1912 and PSS-43)
In "Chapter 3: The Sin", Greef Karga (Carl Weathers) uses a blaster pistol based around a Steyr M1912 modified with the barrel and muzzle of a PPS-43 sub-machine gun. Then in "Chapter 7: The Reckoning" and "Chapter 8: Redemption" Karga uses 2 of these blaster pistols against many of the Stormtroopers, Death Troopers, Scout Troopers, and Shore Troopers of Gideon's garrison.
DL-21 (Charter Arms Explorer II)
A Charter Arms Explorer II modified with a scope and a thicker barrel with the tail section from a British 2 inch mortar shell on the muzzle appears in the Mandalorian's arsenal. This blaster model is known as the DL-21 and despite being little seen or known actually appears in all three original trilogy films to some degree. The original prop was a cut down Armalite AR-7 using a either a modified Sterling SMG grip or a simple rubberised rod of some sort. In "Chapter 4: Sanctuary", one of the farmers uses this pistol during the firefight with the Klatoonians.
A Webley & Scott No. 4 Mk. I with a collar on the barrel is one of the weapons in the Mandalorian's arsenal. This is also one of the weapons that is picked up and examined by Cara in "Chapter 7: The Reckoning".
Walther P38
In "Chapter 8: Redemption" Moff Gideon (Giancarlo Esposito) wields a blaster pistol built around a Walther P38 with it's barrel and front slide assembly replaced with a barrel shroud and fitted with a scope.
EC-17 Hold-out Blaster
The EC-17 Hold-out Blaster is the standard issue blaster pistol of the Imperial Scout Trooper. It is not based on any existing pistol, but rather made entirely for Star Wars.
Unknown
Blaster Rifles
Amban sniper rifle
The Amban sniper rifle is used by the Mandalorian as his primary weapon. In "Chapter 4: Sanctuary", Cara borrows it from the Mandalorian and uses it to good effect. In some of the original concept art for the series, the rifle was built off of an AKM receiver. However, the actual rifle used appears to be an entirely fabricated prop. The weapon was first seen by audiences being wielded by Boba Fett in an animated section of the 1978 Star Wars Holiday Special.
Beretta M12
A Beretta M12-based blaster rifle is seen with armed characters in the season.
BlasTech E-11 Blaster Rifle (Sterling SMG)
The BlasTech E-11 Blaster Rifle, based on an airsoft Sterling SMG, is used by IG-11 as one of its weapons in "Chapter 1". Remnant Stormtroopers use them as their main rifle, sometimes outfitted with tac lights. Moff Gideon's Stormtroopers also use them.
Bren Mk1
A heavily modified Bren Mk1 is one of the weapons in the Mandalorian's arsenal. The original magazine well has been covered over and instead a double drum from an MG34 is fitted to the bottom of the receiver, and a second barrel has been mounted in place of the gas piston tube. In "Chapter 7: The Reckoning", Cara takes the blaster from the Mandalorian's arsenal as her primary weapon. For the series, she acquires it as one of her personal weapons.
E-11D Blaster Carbine (Sterling SMG)
In "Chapter 7: The Reckoning" and "Chapter 8: Redemption", Death Troopers of Moff Gideon's garrison are armed with the E-11D Blaster Carbine. These blasters are also based on airsoft Sterling SMGs, like the E-11.
E-22 Blaster Rifle (Sterling SMG)
In "Chapter 3: The Sin", one of the Remnant Stormtroopers uses what appears to be an E22 Blaster rifle, as seen in Rogue One, this one outfitted with a tac light. These blasters are also based on airsoft Sterling SMGs, like the E-11.
Defense Technologies 37mm Gas Gun
The Defense Technologies 37mm Gas Gun is seen in the show modded as blasters. They appear in several episodes being carried by various background characters along with being present in the Mandalorian's arsenal. They are also the standard weapon carried by a group of Fighting Corps Mandalorians during a Clone Wars era flashback in "Chapter 8: Redemption".
DLT-20A Laser Rifle
A DLT-20A Laser Rifle (built from an Sturmgewehr 44 and a Browning M1919A4 barrel) is used by IG-11 in "Chapter 1" along side an E-11 Blaster Rifle. It also uses in "Chapter 8: Redemption".
A Relby V10 Targeting Rifle appears in the Mandalorian's Arsenal in "Chapter 1". The same weapon appears in "Chapter 4: Sanctuary", where the Mandolorian gives it to Omera (Julia Jones) who uses it to great effect during the battle against the Klatooinian raiders. This blaster is based around a Schermuly Multi-Purpose Gun fitted with twin Sherman Tank gunsights. This blaster was previously seen in the hands of Bossk in The Empire Strikes Back.
Federal Gas Riot Gun
A Federal Gas Riot Gun modded as a blaster rifle is one of the weapons in the Mandalorian's arsenal which is used by a villager in "Chapter 4: The Sanctuary". This is also one of the weapons that is picked up and examined by Cara in "Chapter 7: The Reckoning".
MK-modified Rifle (Dragunov SVD)
In Episode 5, mercenary assassin Fennec Shrand (Ming-Na Wen) is seen using an MK-modified blaster rifle based around a SVD Dragunov (or, more likely, an airsoft replica thereof).
Cycler Rifle (Ottoman Musket)
Tusken Raider are seen with a Cycler Rifle (based on the Ottoman-pattern musket); unlike many other weapons in the series, this one seems more or less completely unaltered, possibly being meant as an actual projectile-firing musket (which the Tuskens are noted to use in some lore sources).
EE-3 Carbine Rifle (Webley & Scott Flare Gun)
The droid bounty hunter Zero (voiced by Richard Ayoade) carries an EE-3 carbine rifle in "Chapter 6: The Prisoner". The EE-3 is built from a Webley No. 1 Mark 1 flare gun that has been fitted with a finned barrel shroud and a scope. This is the variant of the EE-3 that was previously seen in Return of the Jedi (and the special edition version of A New Hope) as opposed to the simpler variant from The Empire Strikes Back.
Bounty Hunter rifle
A blaster sniper rifle is used in "Chapter 4: The Sanctuary".
The Mandalorian's Weapons
Flamethrower
A flamethrower is seen with the Mandalorian mounted on his wrist gloves.
"Whistling Birds" Mini-Missile Launcher
A mini-missile launcher is seen with the Mandalorian mounted on his wrist gloves. The projectiles it fires are called "whistling birds", appear to be guided munitions, and emit a distinctive whistling sound in flight.
Heavy Weapons
Fictional Heavy Blaster
A handheld Minigun-styled blaster machine gun is seen in "Chapter 3: The Sin" with Mandalorian fighter Paz Vizla (Tait Fletcher). The receiver appears to be based on an enlarged MG42 receiver and near section of the barrel shroud, whilst the three barrels are styled on MG34 barrels.
M61 Vulcan
An M61 Vulcan-based blaster machine gun is seen in "Chapter 1" when armed crooks take on the Mandalorian and IG-11. It's seen abandoned in a flashback sequence in "Chapter 7: The Reckoning".
E-Web Heavy Blaster
An E-Web Heavy Blaster is used by Moff Gideon's force during the siege at Nevarro in "Chapter 8: The Redemption". The Mandalorian takes it from the tripod and uses it against Gideon's Stormtroopers.
Oppressor Flamethrower
The Oppressor Flamethrower is seen with an Incinerator Stormtrooper called in to raze the cantina used by the Mandalorian's party to hide near the end of "Chapter 8: The Redemption".
Others
Razor Crest Arsenal
The Mandalorian has an arsenal of small arms inside the Razor Crest. Almost all of them are actual firearms or air guns that are modified to give them a sci-fi appearance. Most (if not all) of these are used by villagers in "Chapter 4: Sanctuary". All of the blasters in the arsenal end up being used by various characters throughout season one.
Jawa Small Arms
The Mandalorian encounters a bunch of unhappy Jawas armed with small weapons in "Chapter 2: The Child".