Fast
Lightweight
Command-line and GUI tools
Supports a fairly large subset of SQL, including indexing, binary objects (BLOBs), etc
Allows changes to structure of tables while running
Wide userbase
Support contracts available
Available for most Unix platforms
Available for Windows NT/95/98 (there are license differences)
Available for OS/2
Programming libraries for C, Perl, Python, PHP, Java, Delphi, Tcl, Guile (a scheme interpreter), and probably more...
Open-source ODBC