They Might Be Giants, henceforth referred to as TMBG, is a band consisting of two main members: John and John. John Flansburgh is the larger of the two, has a slightly deeper voice, and plays the guitar. John Linnell is somewhat smaller, sings higher, and plays everything, though he does a wicked accordion. There are also many many supplementary band members, but since they don't appear on the first four albums, we'll forget they exist right now.
TMBG have released five albums (They Might Be Giants, often referred to as the Pink Album, Lincoln, Flood, Apollo 18, and John Henry) and a B-sides collection, called Miscellaneous T.
The musical stylings of each album are very different: comparing the Pink Album to John Henry will have you wondering if this is actually the same band. One thing remains constant throughout all of their albums, though: their strange and wonderful lyrical nonsequiturs.
TMBG are also TinyTIM's house band, and they have their own plane, Plane 32. (Why 32? Listen to the Pink Album song '32 Footsteps' sometime.) Mind you, the plane only incorporates ideas from the albums up to Apollo 18, but it's still a great place to pass some time.
Of course, if you want the real TMBG experience, go see 'em live. Now THAT's kickin' music. Hope you don't get Ivy as an opening act, though...