Hmmm . . . the OP is missing, but off the top of my head:
Lynyrd Skynrd
.38 Special
GTR
Whitesnake (sometimes)
Bad Religion: Brett Gurewitz (back again), Brian Baker (ex-Minor Threat/Dagnasty) and Greg Hetson (ex-Circle Jerks). Kind of a punk supergroup, if you think about it 
The Eagles
Buffalo Springfield
There was a group (they may still exist) here in Calgary called Superconductor if I recall correctly.
Eleven guitars and nothing else. An experience, to be sure.
Grrrrrr…
I mentioned that the Doobie Brothers once had three guitarists - Tom Johnston, Patrick Simmons, and Jeff Baxter - in the band at one time.
Oops, Greg Hetson is still with the Circle Jerks. I didn’t realize that they reformed again, and are playing on this year’s Warped Tour!
…but as I said, Hetson is still with Bad Religion too. Damn not being able to edit posts!
Greg Graffin at vocals, Brooks Wackerman (Suicidal Tendencies/Infectious Grooves/Vandals) on drums and Jay Bentley on bass round out the group.
Okay; I’ll stop posting about Bad Religion now 
I think the Outlaws had three guitarists, if I’m not mistaken.
Pearl Jam, Radiohead.
Pearl Jam, Radiohead.
outlaws- 3 guitar army
blue oyster cult- on your feet or on your knees
Well, let’s see…
The Travelling Wilburies had George Harrison on lead guitar and 4 other guys on rhythm guitar!
Boston had Tom Scholz on lead guitar, while both Barry Goudreau and Brad Delp played rhythm guitar.
In the Allman Brothers band, you often saw Gregg Allman and Dickey Betts playing regular electric guitars while Duane Allman played slide guitar.
When Crosby, Stills, Nash and Young tour, 3 or more are often playing guitar at the same time (Graham Nash has admitted he sometimes carries a guitar he doesn’t need, or strums an electric guitar that isn’t plugged in, simply because he never knows what to do with his hands while he sings, othewise!).
In the latter-day King Crimson, Robert Fripp and Adrian Belew play guitar, while Tony Levin plays “the stick,” an instrument that’s half guitar and half bass. Thus Levin is essentially playing bass with one hand and guitar with the other. That gives King Crimson the 3-guitar tapestry that’s defined their sound since the 1981 “Discpline” album.
Iron Maiden.
Gregg didn’t play guitar and the only guitar credit for him (at least not when Duane was alive) was for an acoustic guitar.
However, I’m surprised no one has thought of the most obvious:
The Beatles (in the early days, both Lennon and McCartney)
The Rolling Stones (Richards and Jones, and later Taylor and Ron Wood).
The Grateful Dead – Garcia and Weir
Also:
Fleetwood Mac (originally with three guitarists – Peter Green, Jeremy Spencer, and Danny Kirwan)
The Kinks (Ray and Dave Davies)
The Byrds – Roger McGuin, Gene Clark, and David Crosby
Crosby, Stills, Nash, and Young – All four could play guitar.
Traffic – most guitar chores by Dave Mason, but Steve Winwood would play from time to time (listen to some of the songs on “Welcome to the Canteen”)
Jefferson Airplane – Marty Balin, Jorma Kaukonnan, and Paul Kantner all played.
Actually, multiple guitars were quite common in the 60s.
Fugazi.
Metallica
KISS
Bruce Springsteen & The E Street Band
The Go-Go’s
Guns 'N Roses
Mother Love Bone
Kingston Trio
Slayer
Anthrax
Megadeth
In Flames
Rancid
Opeth
and about a million more heavy metal bands…
I’m getting confused… are people counting the bass guitar with some of these choices, or counting bands with two or more guitarists now? There are a lot of bands with lead guitar, rhythm guitar and bass guitar. I thought that the question was asking for bands with 3 or more lead and rhythm guitarists, hence my inclusion of Bad Religion.
how could I have forgotten The Clash !
Stevie Ray Vaughan and Double Trouble.