Another vote for Postgres. Historically, Postgres has been a little more stable, robust, and feature-rich than MySQL, though the gap is closing rapidly. It's also a higher performance database, at the cost of some additional complexity and resources.

I think my preference has much more to do with the preference for the elephant mascot and my anti-microsoftian dislike of "My" in front of program names :)

Still, tons of Linux apps are written exclusively to use MySQL. I'd like to see them written with tools such as DBI, ODBC (pain!), etc, more often so that they are portable and users can choose what DB they want to use.

If it's for learning purposes though, I'd definitely go the Postgres route.

Sidenote: you said you were using the Cygwin version. Looks like a Win32 port is preceeding here: http://momjian.postgresql.org/main/writings/pgsql/project/win32.html. Until then, perhaps (just perhaps) MySQL might be better on Windows. Of course, anything other than MS SQL Server is a good thing :) Also, I believe Informix (disclaimer: untested & I have no opinion) is also free for Win32.