Social Distortion have been a favorite band of mine for about 20 years. While they've only done a handful of covers over the years (that I can think of), I have to say these two are my personal favorites (I'm also a huge fan of the originals too).
First up is their Rolling Stones cover from 1996's White Light, White Heat, White Trash record.
Now here's an acoustic version of them doing Johnny Cash's Ring of Fire. The version on their 1990 self-titled album is more Social Distortion-like, but I thought I'd go with something different.