I'd second the comments regarding SQLite. It's great for what it is - and for most small, no install DBs, it works very well.
There are a couple of other options, though.
Firebird is one option. It has a pretty impressive feature list, and also includes a .net provider (albeit in beta still).
Another option, though not open source, is VistaDB. It's a 100% managed option, unlike SQLite and Firebird (and most other DBs out there), and has a lot of advantages because of that. It's fairly consistent with MS SQL syntax, supports stored procedures, and many other nice features. They have an "Express Edition" that's free, and can be used in open source projects.