Let me add the Wikipedia entry here, I found it most useful:
http://en.wikipedia.org/wiki/Math_rockAs a math rock geek, I would have to say that a few the bands mentioned in the link above are not exactly of core importance to the genre. A list about math rock without Shellac for example is simply incomplete.
Apart from that: I'm a drummer, so rhythmical complexity really appeals to me and straight songs often seem really boring to me, even if the music as such isn't.
For bands, I would recommend: Shellac, North of America, June of 44, Slint, Polvo, Bastro, Don Caballero, Drive Like Jehu, 31 Knots, Ruins, The Flying Luttenbachers (though the later two could also be considered avantgarde jazz or something). Those are the ones I like a lot that I can name off the top of my hat.
For some prime examples, check out:
Shellac -
Didn't We Deserve A Look At You The Way You Really Are - extremely precisely played song with very subtle drumming variation
Shellac -
Song Against Itself - The last part has guitars and bass and drums battling each other rhythmically, only to suddenly find a single beat again
North of America -
Wet to Dance - Excellent transition from 4/4 to 13/8 in the chorus
North of America -
Yes, This Is A Rant - the classic mathy 3/4 to 4/4 and back thing
North of America -
Every Mirror We Broke Was A Black Cat - 9/8, 4/4, 7/8 ... what the hell?
June of 44 -
Cut Your Face - too lazy to add comments from now on
31 Knots -
The Story of Ivan NormalDrive Like Jehu -
Here Come The Rome PlowsIf you want something harder, check out technical hardcore, with bands such as Into The Moat, Ion Dissonance, Botch or Dillinger Escape Plan. Very complex songs that pack a lot of punch too.
Some grindcore bands, such as The Locust and Daughters also have very complex songs, even if it sounds like complete chaos at first.
As for Ruins and The Flying Luttenbachers: Especially the latter are rhythmically so complex that mentioning beats would be useless anyway. This is certainly not for the faint of heart, but if you like complex time signatures, you will love them.
If you want to, I can hook you up with links to tons of free (and legal) MP3s, but I'm too lazy to just post them here without any certain interest.