As mentioned, the FBI currently issues new agents a .40 caliber Glock 22 or 23 upon graduation from Quanitco. I think they are either issued or allowed to carry a Glock 27 back-up. Maybe I'm wrong, or maybe the info is opsec sensitive.
The FBI used to issue 9mm Sig Sauers, models 226 and 229 (maybe 228). No longer. They also briefly flirted with the SW 1076 in 10mm, a cartridge which was developed specifically for them. That didn't work out so well. Even earlier, the Bureau issued .38 Caliber Smith and Wesson Model 10 revolvers... at least I think that was the model number.
As I understand it (I might be wrong), agents can carry whatever they were issued. So there might still be a few kicking around who carry wheel-guns. I am also of the understanding (might be wrong) that there are other approved weapons. For instance, an agent who is issued a Glock might choose to carry a .40 caliber SIG 229 if they buy it. Kimmi could probably confirm or deny that.
FBI SWAT agents are issued the Springfield Bureau
Model. As far as I know (and I don't know everything), they are the only Feds allowed to carry 1911, although I do know the US Marshal SOG gets Springfield Operator .45's, so maybe I'm wrong. Also, I think FBI HRT operators are allowed to choose whatever sidearm they want, though most choose that Springfield Bureau model. They used to be issued .45. cal Para-Ordinance 1911's, and before that it was Browning Hi-Powers in 9mm.
Long arms. FBI agents also have access to MP5 SMG's, which I believe are/have been phased out in favor of M4 style carbines (I think they might use the DEA Model Rock River carbine). They also have access to Remington 870 12 gauage shotguns. And of course, SWAT Teams, Regional Enhanced SWAT Teams, and the HRT have everything from Remington 700 sniper rifles and P90 submachineguns to grenade launchers, Barret .50 cal anti-materiele rifles, and yes, even Squad Assault Weapon Machine Guns.
Local cops carry virtually every sort of mid to full size 9mm, .38 caliber, .40 cal and .45 cal handgun under the sun. I think by numbers the front runners are Glock, SIG Sauer and Heckler & Koch. Maybe Smith and Wesson is in there.
All of my information has been gleaned from open source, so much of it may be wrong. Anyone who knows better, feel free to correct it. (I'm looking at you Kimmi)
Also, if you're curious about other federal law enforcement agencies, let us know.