Many media players, including Windows Media Player, can't handle .flv videos downloaded from YouTube. FLV Player offers a simple solution. It's a straightforward media player with one single purpose: playing .flv files. To open a file, press Ctrl-O, browse to the file you want to play, and open it, or else double-click the .flv file from inside Windows Explorer. You can also drag and drop files into the player. The player even lets you play multiple .flv files; simply drag several files to the player, and it plays each in its own window.
You can control video play via the usual controls, or a variety of keyboard shortcuts. You can also toggle back and forth between full-screen mode and normal mode. Note that you may run into problems installing the software on Windows Vista. If that's the case, right-click the installation file, and choose Run as Administrator. That should solve the problem.