I think you should ask what a personal domain actually is. In my opinion, it's a website about YOU. Not just who you are, but also your interest, hobbies, likes and dislikes. When someone goes to you.com, they are intentionally interested in YOU.
Boiling it down to what you asked, I think the question then becomes "What do I want to share with the world?" And it is truly the world. As you've said, you don't want too much personal information out there, but a website about you doesn't have to be just the facts about you.
I've thought about this recently for my own site. I don't care to be a blogger either. Here are some things I can think of that might spur on your creativity:
1) Articles - write articles on things you like. These aren't blog entries per say, although they could be. But if you find yourself interested in some topic, and would like to write your ideas down, an article could be a good avenue for that.
2) Works/Portfolio - if you have a hobby or career involving something that you can show off or demo, put it up there. If you are a photobug, put your favorites pics up, or if you craft things out of wood, take pictures and put them on your site, etc, etc. Find out what you like to do and/or are good at and share it with us!
3) Personal Photos/Videos - photos and videos say a lot, but they don't necessarily give away your information. Pictures of yourself, friends, family, co-workers, places you go, things you eat. Anything.
4) Resume - an easy one. Could also expand it to include links to companies you've worked for previously or links to works you've done.
5) Profit!! - Hope you enjoyed that oblig. slashdotters. Ok, snap out of it, this isn't a step-by-step thing. But seriously though, if you have a lot of junk in your house you need to get rid of, you could use your site as real estate for selling things. Not really a long term idea -you might run out of stuff to sell- but it could work.
Remember what web pages are: text, images, videos, sounds, colors, interactive media.
Take what you like to do and want to share and apply it over those mediums.
It's a personal domain, so make a personal site! When I go to you.com, I want to know about YOU!
Hope I helped.