My highest level was 11, but I've seen people get over 6,000 points, so I'm assuming that there are many more levels to conquer. I don't see how it's possible.
On my best game I was 6 cards away from completing level 20. I have reached level 20 only a handful of times. I find I have a hard time getting past level 15 if I am on a machine with a slower internet connection. It helps to have speed on your side or the cards flip over too slowly.