C. Start off building on top of one of those platforms to get a jumpstart on gaining audience. But plan your strategy so you aren't dependent on them, and have a stable future even if they disappear completely tomorrow.
Some services (like url shorteners or photo uploaders) that are entirely dependent on the platform to be useful probably can't work in that model. To them I would probably say: get big and hope to cash out before it's too late.
Lots of people have tried this. It's very hard, especially on Facebook, because people are there to spend time on Facebook first and foremost.
The one exception to this might be Zynga, but of course they're far and away the #1 app developer and I'm sure some non-trivial percentage of Facebook users come back to the site just to play Farmville.
Exactly. I don't know why more haven't been doing this. Ev must have been very persuasive about the ecosystem that everybody was building. Funny, the Twilight Zone episode "To Serve Man" just came to mind.
B. Start from scratch. Spread by word of mouth. Try to get media coverage. Risk getting lost in the crowd.