Sometimes students ask me if they should include "personal projects" in their portfolio. To me, it depends on the project. Short stories, no. A few pages of design or photography, sure. Taxidermy, maybe not.
Your website, though, now that's the perfect place to show off your other talents. A creative director isn't necessarily looking for it, but side projects can give a better sense of your personality. I know a lot of people who divide their site between WORK and PLAY, or just have a "personal" section.
Creatives are usually good at coming up with cool ideas for projects and then really bad at following through with them. But here's a guy I went to school with who has a enviable list of non-ad projects and stuff on his site. His name is Todd Lamb.