Here's a few "popular" tunes on different instruments tuned in slightly unusual ways: 1) "The Hangmans Reel" played by Aly Bain on the fiddle tuned AEAE. This is quite a common fiddle tuning if you want a drone at the bottom end. 2) "Brass in pocket" by the Pretenders. The bass is tuned DADG. This was in the days before 5 string basses really took off. 3) "The first cut is the deepest" by Martin Simpson on the guitar tuned DGDGBD. Most of his tunes are in unusual tunings and very kindly he usually tells you what they are on the sleeve notes - he sometimes even gives the tab.

I've personally always felt that there is no "standard" tuning for an instrument. If it sounds right then go for it. I think that if you are providing an accompaniment for a singer then the key that the singer chooses, timbre of their voice and the mood of the piece all affect the choice of tuning (I'm talking about the guitar here).