Pushups
 

I have heard that pushups are the best way to build up my arms. That they are even better than lifting weights (which I would not stop doing, so dont get me wrong) This true?

Push-ups will build your arms up some, but after you're able to do a lot of them, they won't provide the kind of gains that other movements would. If you want a bodyweight movement to build triceps, I would go with parallel bar dips personally. And once they get easy, you can add a belt and hang weight plates off of it.

If you like pushups, and can do a lot of them, try weighted pushups, with a plate on your back. Or, as brute says, parallel bar dips.

Or a backpack with plates. Or a child(ren).