Twitter and eBay both had significant web presence and community before their APIs took off. So did Facebook. Only once you have something worth getting at will people want to integrate with you.

To be fair, a lot of Twitter's success was due to their API, but without a decent minimal web presence, nobody would have signed up. Remember, everybody's first Twitter client was the web. If that sucked, or didn't exist, nobody would have bothered to pick up an API-based client.