Ped sounds right on to me. I always tried to ignore tantrums as much as possible and, as a result, DS (5) next-to-never tantrums now. In fact, I think we've only had two or three big tantrums in the last year. You would think by 5 that most kids wouldn't tantrum anymore, but wow! You should see some of my friends' kids! Some of them still tantrum daily!
The less you pay attention, the more they realize a tantrum won't get them what they want.
However, it is tough out in public to use this technique. People look at a kid lying on the sidewalk or on a store floor screaming, then look at you like you're a terrible parent. In this situation, I always tried to remove my son from the scene as quickly as possible. I remember a few wicked tantrums in the car seat.
However, don't make the same mistake as the woman in Riley's post and leave the kid screaming in the middle of the parking lot! Not recommended! :D