I dunno what "real" artists are supposed to draw, but I doubt they draw a lot of characters from movies and tv shows. But I've always enjoyed drawing my favorite characters - maybe the fact that there's a story behind them makes them more interesting to draw.
This is Zoe from the most excellent but short-lived tv show Firefly. I like her because she doesn't say much, but when she speaks up she usually has a very dry sense of humor that she delivers with an absolutely straight face. She is also happily married - which is unusual for any character on any tv show.
I'm still working on my portfolio for the Academy of Art. I think it's getting near to being done!