Take a 5/4 drum beat.
h:--x---x---x---x---x---
s:----------x-------x---
b:--x---x-------x-x-----
Each hi-hat hit is one beat. It's a really simple beat, but you can tell it's 5/4 very easily. And it's probably just as easy to put something to it. 5/4 is made up of two signatures, 3/4 and 2/4. This gives this time signature a sense of incompleteness.
Also check out bands like Az said, like meshuggah and also quite a few 70's classic rock bands use odd time signatures.
"My whole life is a dark room...ONE BIG DARK ROOM" - a.f.i.