Google and Microsoft have competing services, but those companies also suck. I think they're less popular, but I don't know much about why.

I'm not aware of any smaller competitors, though some probably exist. It would be a big risk for a company to go with a new provider. There's a lot of library support for the big players, for one thing. If you want your python application to talk to AWS, the boto library is just right there.

You could run your own hardware somewhere, but that has its own host of problems, if you'll pardon the pun. I worked somewhere a long time ago that had its own servers in a data center. The place got flooded in a big storm and we were down for a couple days.