I've read a lot of database books in my time, and been around some of the biggest rdbms instances on the net. Here's probably my top three:
1) If you don't know SQL, O'Reilly's _Learning SQL_ is the best intro I've seen. This doesn't sound like what you're looking for, though.
2) If you know SQL reasonably well, but you want to get much better, I can't recommend O'Reilly's Theory In Practice book _The Art of SQL_ highly enough. I don't have it in front of me to remember precisely why I liked it so much, but it's outstanding. If you're going to get one book, get this one.
3) To really get the theory of databases, one of CJ Date's books is good. Someone else recommended _Databases in Depth: Relational Theory for Practitioners_, and I recall that looking pretty good when I skimmed it once. I would also recommend _Foundation for Object / Relational Databases: The Third Manifesto_, which I found to be very educational. You need to be careful with Date, though, because he tends to advocate how things "should work", not how databases actually work, and so you may find him advising you to do things that are actually bad ideas on your database of choice, so balance this off against good books for your specific DB
4) If you need to build large data warehouses (doesn't sound like you, yet), then Ralph Kimball's _The Data Warehouse Toolkit_ is all you will need to understand the theory. Unfortunately, effective warehousing is especially tied to your database of choice, so you'll want to hit the product manuals even harder here.
5) If you need to do OLAP (also not likely), there's only one generic book that's particularly good at all for the concepts, _OLAP Solutions_ by Erik Thomsen, and even that is not that generic. Unfortunately most OLAP and BI stuff is highly vendor-specific.
Joe Celko's books are also pretty good, in my experience, but I wouldn't buy them before the above.