Windows Media Player is acting strange...?

I have downloaded some media files, both movies and songs, from the internet using the Vuze program. When they are done downloading and I open them and play them with media player, they work just fine. But once I close Media Player, and then reopen it, those files are no longer there. This is true even when I make a playlist including those downloaded files. Also, there are some playlists in media player that I cannot seem to delete...