Our founding fathers just didn't realize the ongoing problem they were creating when they adoped a name. At the time there was not real combined identity or name. So we ended up with USofA & forever wonder what to call ourselves. Others don't know what to call us either. I try not to call myself American, but there's no good alternative & I notice people abroad will call us Amercans anyway.

As others have noted there's not really much difference in US or USA for writing. I'm more likly to say United States alone; US if it's a modifier--US Hockey team, etc.