Apple uses QuickTime to play videos. This software is built in to the Mac OS X operating system. The "Software Update" under the Apple menu will make sure you have the latest version. I believe that Adobe Flash comes preinstalled on the Mac, but it might need an update. Windows Media is the other major format, and that definitely requires additional (free) software. Very few people use "Real Player" anymore so I would not install that.
If you need Flash, go here:
http://www.apple.com/downloads/macosx/internet_utilities/adobeflashplayer.html
Flip4mac lets you play Windows Media files on your Mac. You can get the installer here:
http://www.apple.com/downloads/macosx/video/flip4macwindowsmediacomponentsforquicktime.html
I also recommend Perian, which adds additional media types for QuickTime.
http://www.apple.com/downloads/macosx/video/perian.html