Short bio: Computer Scientist, FOSS supporter (read more)
Tux Machines (TM)-specific
List price: Free to download and use (support extra)
Made by: MySQL
Pros: Free; Loads of new features over 4.1; Excellent support for a range of platforms; Performs well in small and medium applications
Cons: You probably wouldn't use it for a big, heavy-duty installation
Buying advice: MySQL has always been an attractive option, and continues to be so. If you're already running it, you may as well move to 5.0 as it seems stable and the update path only gets complicated (and then only slightly) if you're using replication.
MySQL is by far the best known, and most popular Open Source database engine. It ships with most Linux distributions (not to mention commercial Unix incarnations such as Mac OS X) and has become immensely popular over the years because it's an ideal way to run a decent-sized database at minimal cost.
As a developer, though, I've had to work around some fundamental flaws over the years. My main gripe about MySQL so far has been that it hasn't supported stored procedures. These are user-defined procedures that you build into the database itself and then call from client-end applications - so you define stuff once and can then call it from a number of client platforms. Buzzword enthusiasts call this a "multi-tier" approach; think of it as "write once, use many".