I use my thumb extensively in my playing, though I hold my guitar in a standard fashion. I use my thumb a lot in chord melody playing to hold a bass note while I fool around with my other 4 fingers. I play some classical music, and though you're not supposed to, I use my thumb for it. One outstanding example I have would be Bach's Bouree in E Minor. Now the way I play chords and such, I can't think of a way to NOT use my thumb. Check out this chord, which I use often (keep in mind, you can use any note on the 6th string as a root. I'm using A for an example). 5, x, x, 6, 5, 4 = Amaj7
I use this type of chording extensively and it really helps me make some beautiful chords, which I otherwise wouldn't be able to reach.