I greatly enjoyed Dysfunctional Family Circus, and there's always Gorefield, aka Garfield written by Lovecraft. Garfield was always a little boring, though--I think I was in second-grade at the time.

Have you delved back into the old classics? There's a lot there. Sometimes it just takes a little while to learn what the comic is about--is enough to do when you're exposed to it every day in the paper, but harder if you're going in blind. I don't really think of comics as greatly in need of innovation, though phone accessibility is a factor, I can´t think of anything that is better for being on a phone.