Me too. Like Solomon's Keep, which just has two joysticks. One for movement, one for firing. And the Zenonia games have something nice control-wise, because you can adjust them however you want - even make the d-pad different sizes.
I liked Knights of Pen & Paper, which is turn-based.
In terms of puzzle games, I tend to go for word games. A few I've liked are: Bee Spelled, Textropolis, DecoderRing, and Psychobabble.