I was parking my car at a busy gas station and hit a curb. The guy behind me said that I hit his car, but I said I didn't. None of the other customers witnessed anything, (it was full that day) and the police were not called. Am I liable for his "damages"?

I would think that the gas station would have a survalance camera in which case weather you did or did not hit his vehicle would be on film.. it's his word against yours and if there is any proof( such as your paint on his car) I would think he would have called the police and filed a report. I would ask the gas station if they do indeed have footage of that day just to cover yourself.

You need to report this to your insurance company immediately. They will take care of it.