I'm pretty much with chicagodoubler on this one. I use drop D sometimes, and might tune down a half or a whole step if it fits the song. (There's too many funk songs in Eb and D...

) That's about it.
It's more of a guitar thing to tune to different tunings. It's more understandable there as they're used to create chord voicings that are practically impossible to play in standard tuning. And you play mostly one note at a time, don't you?
EDIT: Oh, a few years ago I had my bass downtuned a whole step for perhaps half a year and played all gigs with that tuning. There wasn't too many disadvantages with that, but for some reason I switched back. Think it was because when reading chord charts of new songs, I had to re-think where to put my fingers all the time. Once I knew the song, there was no problem anymore.