Which DBMS are fast enough for an online game (few thousand players)? I'm currently making an MMORPG game, which could have a few thousand players online at the same time (probably not; just wishful thinking). First we wanted to use MySQL, but I have heard it isn't fast enough for this scale.

Which DBMS is fast enough? How much like SQL Server is it (as I have learned SQL Server in school)?
This is a really tough question to answer. You can take the fastest database platform in the world, design a horrible schema, write a crappy application around it, and then be tempted to blame the database platform. At the same time, you could take the free SQL Server Express and, with the right design, application logic, and an approach at sensible scalability (e.g. scaling out reads by data caching, etc), you could write an application that handles 1000s of users no problem.

Do I believe SQL Server can handle 1000s of users? Absolutely. Do I believe Oracle and DB2 can do so as well? Certainly. MySQL? Not sure, not enough experience there. Access? Probably not a wise choice at all. If you are familiar with SQL Server, then I suggest that is the route you consider, just keep in mind that your choice of RDBMS will not in and of itself dictate success or failure.