I've written a little in alternate tunings and I know several cover songs that use alternate tunings.
Alternate tunings are not new. Some big names who use alternate tunings include Led Zeppelin (Jimmy loved DADGAD), Joe Walsh, Soundgarden (most of their songs are in alternate tunings), Rolling Stones.
I see two real benefits to alternate tunings:
1) They sound "different" than chords voiced in standard tuning. Much like an open G chord (in standard tuning) is a different flavor than a barred G chord. So basically you get slightly different flavors of the same old boring chords we are all used to hearing.
2) They allow you to do things you couldn't do in standard tuning. Alternate tunings create pivot points and intervals that would be impossible to finger in standard tuning.
The only real disadvantages that I can think of relate to playing live. Although, some tunings may make it more likely to break a string and some tunings are basically impossible on an
acoustic guitar (try to tune the G string on your acoustic up to a B and you will understand).
For live playing, you have to take time to re-tune if you are playing songs in both standard and alternate tunings (or various alternate tunings). I always bring at least one extra guitar so I can have it tuned up and ready for the song using an alternate tuning. I will even plan the set list around songs with alternate tunings so that I can minimize tuning time and changing guitars.
Here are some fun ones to play around with (there are many more):
DADF#AD
DADGAD
CGCGCD
EEBBBB