It's copyright infringement, so yeah it's against the law, and against Youtube TOS , but most of the time if YT gets a complaint they just remove it. You don't really have to worry to much, the first time they just remove the video and not the whole account.
Edit by me:
There are ways around copyright, like if you chop out pieces of the music video and use it in say a remix. The remix can contain lots of different videos but would have to in a way look like your own original work.