Is it illegal to put NFL,NBA, and MLB games on youtube?

It's complicated. Copyright law allows you to use short clips of copyrighted material (which ball games are) for purposes of commentary. This is called "fair use." Sometimes a copyright holder will challenge this and then you might have to sue them to repost it, but, short answer, no, it's not illegal to post CLIPS from ball games. You can't post the whole games, even with commentary.