What can the use of odd, interesting, or changing time signatures add to a peice of music?

I recommend listening to Dave Brubeck's Time Out. That whole record is an exploration of odd time signatures and unusual ways of subdividing rhythms, but in a way that still swings. Three of the more famous tracks, for example, are:

"Blue Rondo a la Turk": This is in 9/8, which is an old time signature dating back to the Baroque period, used when a composer wanted a triplet feel in 3/4 time. What makes this song different is that instead of the usual 3-3-3 break-down, Brubeck subdivides the beat into 2-2-2-3, which gives it a totally different feel.

"Take Five": This is in 5/4, subdivided into 3-2. You've heard this song a million times, even if you didn't know it. It's in every commercial that's trying for a "sophisticated luxury" feel. It isn't easy to make 5/4 sound mainstream, but this song does it.

"Three To Get Ready": This has a pattern of changing time signatures throughout the song. It's two bars of 3/4 followed by two bars of 4/4, then back to two bars of 3/4, then 4/4, etc. The drumming is interesting here: Joe Morello basically just brushes a 3/4 pattern on the snare during the whole song, but in the 4/4 bars it starts to syncopate, which then causes it to be "out of phase" in the 3/4 bars, gradually coming back into phase later.

Anyway. It's a great record and a wonderful collection of odd time experiments.