Bluegrass banjo is played on a 5 string banjo. The standard tuning is Open G Tuning (G, D, G, B, D). Although the vast majority of bluegrass banjo recordings have been done in G Tuning, or with a capo in G Tuning (Earl Scruggs actually did a number of recordings with his banjo tuned up half a step to G#, so it was essentially open G# tuning - G#, D#, G#, C, D#), there are a number of other popular tunings used.
Here are some of the more popular ones along with a video example.
Earl Scruggs used this tuning a fair amount. In this tuning you can choose to tune the 5th string either down to F# or up to A. He also used his legendary D Tuners to slide the 2nd and 3rd strings to this tuning and back mid song in tunes like Earls Breakdown.
Reuben is one of Earl Scrugg's most famous tunes recorded in D Tuning
This is very similar to D tuning except that the F# notes in D Tuning are now tuned down half a step to F to make the minor sound. Just like in D Tuning, you can choose to tune your 5th string down to either F or up to A.
Here is an example of J.D. Crowe playing Nashville Blues in D Minor Tuning (with his 5th string tuned down to F)
This tuning is sometimes called C Tuning, but it is really Drop C Tuning because we are "dropping" the 4th string down one whole step from D to C. Earl Scruggs used this tuning a fair amount. His recording of Home Sweet Home is a good example of this tuning.
This tuning simply tunes B string from the Open G Tuning down half a step to Bb to make a minor sound. Listen to Bela Fleck play Natchez Trace in this tuning.
There are plenty of other tunings that bluegrass banjoists have played in. Enter some of the others that you know of along with a link to an example in the comments below!