My student Bianca has been working on accompanying herself singing, either with piano accompaniment or guitar. She's become pretty good at it, to the point of inspiring her examiner to clap and say "Brava!" at the end of her examination performance of "Teardrops from My Guitar". She's been one of my inspirations for doing the same - for gigs though, not exams. Here are some sites my students and I have been using for our chording and singing purposes:
As I mentioned in a previous post, it's a great way to practice ear training. It's really tricky trying to sing on pitch while only playing chords.
September 3, 2020 update: I updated some of the links as the old links were defunct.