<p>Question says it all, really. 
My application is a time tracker.  It's currently written as a spreadsheet, but there's just too much data and I would like to impose a bit more structure on it.  </p>

<p><a href="http://sqlite.org/" rel="nofollow noreferrer">SQLite</a> seems like a neat way to go.<br>
I would be open to other suggestions, too.  </p>

There are some providers available:
http://sqlite.phxsoftware.com/
http://sourceforge.net/projects/sqlite-dotnet2
And you can get up and running in just three minutes according to this chap:
http://www.mikeduncan.com/sqlite-on-dotnet-in-3-mins/
Updated Jan 5 2009:
We actually have this rolled out to our shared (partial trust) hosting environment and it works really well according to early customer feedback.