I want to buy an Ipod but is it true I can only play Itunes videos on it?

I want the nano or clic but Ive read that you cant put other videos on there even if they are in the proper format, that you have to buy them off Itunes.I know there are third party software converters but my question is if I convert an Avi or wma to ipod mp4, will I be allowed to watch it on the Ipod?