I would absolutely pay for this. I'm a hypochondriac and think that I'm just about to die for a different reason every day, and have a fear that some people that I keep in contact with on the internet simply won't know until years after the fact.
The company would have to be extremely trustworthy to get my passwords though, and that'll be a tough hurdle. The key to distinguishing yourself would be a great UI with sensible (well researched) defaults and offers of form letters.
But $10-$20 bucks a year? Done.