Q:

Vulnerability check via web interface?

Is there a website I can log into that will can check various exploits on my system, and basically tell me if it's patched up-to-date?

A:

I think you would be better of by installing Nessus on your own computer. Nessus is free for home use and have a commercial version available too, and it lets you actively probe servers with a wide range of plugins.  
Check it out: http://www.nessus.org/nessus/
Also.. could you trust a public webpage that probed your computer for errors? Setting up such a server would probably mean lots of problems for the host, since it would trigger IDS-alerts from other network providers. And you have no guarantee that they won't abuse their findings.
EDIT: Didn't know that they had changed the license on the plugin-feeds. Thanks K. Brian Kelley. Still worth it though. Superb software.

