Three note chords are a nice background to vocals. Also, when playing a second rhythm guitar, they don't flood a song with too many notes. The three I'm going to show you and some variations are ones I like to use a lot. They're movable, and, as you'll see, they give you a nice base line when played at the 9th fret. On all three, the lowest string (in pitch) is the third degree of the scale, the next higher is the fifth degree of the scale and the highest is the root. As I said, they can move all over the fretboard and are defined by the position of the string with the highest note. So here here is an A chord (defined by the 2nd string, 10th fret, the root on the A note):
Notice, on this a chord, that 5th string, A, is open, so this can be used (only at this position!) as a nice bass line contrasting with the higher pitch of the three note A chord. You can also drop your pinkie on the 5th string 12th note and you still have an A chord albeit not quite as interesting. Don't forget, though that you can move this all over the fretboard as a three note chord.