EPT
I want to make a blog though dedicated to that, and try to maintain a decent compilation for your enjoyment. If you have anything to contribute with, please share! I'll start with some of the best that come to mind, have fun 
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Improv Everywhere - "Long form improvisation troupe that executes pre-planned "missions", usually involving socially awkward or unusual situations." Probably most famous for their Frozen Grand Central: + Show Spoiler +
Simple Pickup - Group of 3 guys picking up girls in very awkward / funny ways. My favorite is this one, which has StarCraft as it's theme: + Show Spoiler +
PianoChatImprov - is his channel name, and he does all sorts of cool stuff in public involving him playing his piano. Probably most famous for his Chat Roulette sessions: + Show Spoiler +
Now that I just linked a chat roulette video, this one just came to mind. Not quite public, but it was a "random stranger". These Danish college students set up a marriage proposal to a random girl over chat roulette for their school project in internet virals. + Show Spoiler +
ED Bassmaster - Funny individual who does all sorts of weird stuff in public. + Show Spoiler +
Athene - Doesn't really specialize in street comedy, but he has outbreaks in a few of his videos which I find hillarious, such as this: + Show Spoiler +
MLG Anaheim 2011; awkward interviews of girls performed by Edward Starcraft + Show Spoiler +
