Doing squats, lunges, deadlifts, and clean and jerk, I like a low heel-to-toe drop with minimal support so you have a flat base for your feet. The most popular shoes for these kinds of things are Reebok Crossfit Nano and New Balance MX20. I prefer the Reeboks because they have a rubber on the sides of the shoes that I feel help support lateral movement. The sides on the New Balance are more mesh.
Some people like the Nike Free 3.0, but I've heard they don't last as long.
I wouldn't use any of these shoes for long distance running though, because I don't believe the "free run" shoes are a good idea.