Has Foursquare succeeded? From what I've heard, they aren't profitable, yet, which means to me that the jury is still out on them.
They have a loyal and relatively large user base and a lot of mind and market share. They also have a feature set that most of their competition is now trying to emulate. They seem to be headed in the right direction but their success as a "company" is still to be seen.
Also for perspective, I can't, off the top of my head, think of a mobile geolocation service that I would consider more successful then Foursquare. I could easily be missing something though.