MySQL itself is open source and can be used as a standalone product in a commercial environment. If you're running mySQL on a web server, you are free to do so for any purpose, commercial or not. If you run a website that uses mySQL, you won't need to release any of your code. You'll be fine.
mySQL has enterprise licenses with (I think) a different code base, and premium support by Sun, but those are entirely optional.
There are limitations on redistribution of mySQL within a closed source product, and linking against mySQL libraries as was pointed out in a different comment. As for redistribution:
OEMs, ISVs, VARs and other
distributors that combine and
distribute commercially licensed
software with MySQL software and do
not wish to distribute the source code
for the commercially licensed software
under version 2 of the GNU General
Public License (the "GPL") must enter
into a commercial license agreement
with Sun.
if you are looking to redistribute mySQL along with a commercial product, check their legal page. I think most companies circumvent this by installing the mySQL server separately.
GPL and linking against client libraries?
I don't know what the fact that the GPL (the license mySQL is distributed under) forbids linking against closed source software means for applications that do not link against mySQL directly, but ship with mySQL client libraries. Do those have to be Open Source? If anybody would like to shed a light on this, in a separate answer or a comment, I'd be most interested.