Two year old son has a temper!?

My two year old son has terrible temper tantrums and throws things. He does it when his father doesn't pay attention to him(which my husband does unless he is getting ready or doing something where he can't hold him) He also does it when he doesn't get to go outside, or doesn't get something he wants. He cries for long periods of times when he wakes up and at times if he wakes up during the night. I tried "time out" and still no luck. I have been just ignoring him and letting him cry, but it seems he does it for longer periods of time and it is very frustrating to me. I thought if you do not reinforce the negative behavior it is supposed to extinguish itself. At least that is what all my psychology education has taught me. HELP...what do I do?