I really enjoy database design and the whole concept of managing data semantically and all the logic that comes with it.
My knowledge level when it comes to databases is
A whole other area is dimensional modelling and data warehousing.
I had been working with relational modelling for years, and then I read The Data Warehouse Toolkit and received an entirely new view of how it could be used.
Get more dirt from C. J. Date's Database In Depth: Relational Theory for Practitioners if his An Introduction to Database Systems isn't grubby enough for you.
Seriously, these two books will give you a great deal more knowledge about RDBMSes, in a great deal less space, than many other professional database workers possess. Database in Depth, in particular, looks at how to think about databases relationally even when the language doesn't support it, and how to trick SQL into being a close-to-relational language.
A very common scenario is having to map ugly databases to an entity model which is not necessary reflected directly in the structure of the DB. Working out which way is best to model the data in your domain can be tricky.
Full text search and XML are subjects that seem to be coming up more and more.
I have no experience with it but I know DB2 (of which there is a trial version) has some crazy new features)
Have fun :-)
There is only one rigorous technique for conceptually modeling a relational database schema that I know of (and I've spent a lot of time looking). It's confusingly named "Object-Role Modeling". Here are a couple references.
http://www.agilemodeling.com/artifacts/ormDiagram.htm
http://www.tdan.com/view-articles/5033
http://en.wikipedia.org/wiki/Object_role_modeling
http://en.wikipedia.org/wiki/NORMA
and here's a plugin for Visual Studio
Don't forget representing hierarchy and/or graphs in databases. It can be a pain & there's no right answer.
The standard techniques (for hierarchy at least) have been mentioned in these SO posts:
edit: There's also spatial database applications for GIS use, where you have data structures and/or indices based on point locations using R-trees and the like. Using these is a little bit different than the regular non-spatial database features.
being just a student of Databases I can only speak from my limited scope but I can suggest two sites that may help...
http://database-programmer.blogspot.com/2008/09/comprehensive-table-of-contents.html
This is Kenneth Downs site, he goes from the very basics if SQL and delves into more complex subjects. The man has written a framework around DB's after all.
Another one is High Scalability...
http://highscalability.com/
They get into every realm of DB's.
Hope this helps.