I save seed from tomatoes and beans, always. I've also saved pepper seeds, just to see how they would do... and even the hybrids came back from those seeds essentially identical to the parent, as far as I could tell. I think it's pretty common for the "F2 generation" of a hybrid to be pretty close to the parent; but then each generation becomes less and less consistent. Even so, it can be fun to experiment with...
This year I'm also saving seeds from my Danvers Half-Long carrots; a couple of the carrots I had stored over the winter got planted back into the ground, took off growing again and made seed stalks. I definitely don't have any other carrots that have gone to seed, but there is Queen Anne's Lace in the area, so hopefully they won't have crossed. Maybe next year I'll give beets a try.
I've also saved seeds from winter squash, when I wasn't growing another one of the same species; haven't yet ventured into isolating and hand pollinating them, although it doesn't sound terribly difficult. And I've saved seed from ornamental corn, when I wasn't growing some other type along with it.
