Not quite sure, but I think the levels are just a different representation of the total points you have received in that language. So, I guess there is no maxium level.

I think the maximum level is 20 (but I am not sure). You gain many points reviewing, translating and similar, you could have not made one lesson but reach level 20 nonetheless if you would translate all day long. :D

I'm not sure what the maximum level is, but I know it goes at least as high as 25 (one of my friends is level 25, I'm level 23). :)

I can tell you that I tested out of the entire German skill tree on day 1 (I'm a German professor) and was put in Level 11, so given that there are 25 levels possible across duoLingo means that apparently one's "level" does not exactly indicate how well you know the language. It's more an indicator of how much work you've done on duoLingo.