Wow--I can feel my bp rising just thinking about this issue. My dd has been doing this behavior forever (she's 25 months). At first, it was just her way of expressing herself and letting off steam. She was a fussy baby, so a noise that was happy and not a loud crying fit actually sounded good to me, even if it did attract a lot of attention from others
I had chosen to adopt the ignoring approach--my gut told me not to make it an issue--but she started "teaching" her friends to scream, and their parents wanted them to stop. I knew they would never stop if dd was allowed to continue right in front of them. Then it became the big, ugly "use your inside voice" issue: yet another toddler power issue. And now we have 6-wk-old ds who doesn't think much of it.
Lately, the approach has been to ask her to apologize when she does it anywhere but in appropriate or designated places (one room in the house, at the park or outside, and in the shower), especially if it bothers someone. If she continues, I'll take her somewhere appropriate and have her do it there: often she won't, because it's not fun without the reaction from me. That's definitely the hardest part: controlling that reaction and trying to make it a non-issue whenever possible, especially when there are others around who don't take that approach first. Sometimes ignoring the behavior can still diffuse it before it escalates.
It's great to read other ideas, too.