DungeonMasterOne is correct. The copyright owner must give permission for his work to be used in anything that might be redistributed. This makes sense for at least 2 reasons. The first is the one already stated by DungeonMasterOne; you're redistributing the artist's work. The second one is that the artist may or may not want his work associated with your work, or you might be reproducing a low quality version of his work, etc. The original artist has a right to protect the integrity of his/her work.
If you really feel what you are doing is harmless, the answer is very simple. You simply contact the copyright owner and get written permission. There's a slim chance you'll get a large record company to give you permission, but smaller artists might simply ask for a credit, in that you may be promoting their work.
The rules with the original copyright laws were fairly common sense. They get complicated in the gray areas and really convoluted when you start studying case law. There are some areas where it's pretty black and white, though. For example, I can't license a recording for personal use and then put it on YouTube for the whole world to enjoy. Note, that when you "buy" a song, you are not really purchasing that song, but rather entering into an agreement with the artist that grants you the right to listen to that song with restrictions. i.e. You can't just play the song in your restaurant to entertain your patrons, unless you pay performance royalties. That's where it starts to get complex, but posting it a website is definitely out! ;)
Since the original copyright law, the law has been revised and the DMCA has been enacted. Things aren't as simple as they used to be, but you may assume that the changes made the law more restrictive and the penalties for breach more severe, rather than less. DMCA did a lot to handicap "fair use". At one time, if you purchased a VHS movie and later decided you'd like to have that movie on DVD, you could have copied it to DVD for your own personal use. Now, that would require circumventing built in copyright protection, which would make that act illegal. Personally, I am going to do whatever I want within the walls of my own home, but once you start advertising your disregard for intellectual property laws on the Internet, you're opening yourself up to some nasty litigation.
In a nutshell, I'm with DungeonMasterOne. Don't use anything in your videos that belongs to someone else unless you've got written permission. I have a talented musician and composer who works with me when I need a music bed for a documentary or something. Otherwise, I make simple riffs in GarageBand, or simply avoid any music. It's also a good idea to watch for copyrighted images, TV broadcasts, etc. that might appear in your videos.
It sucks, but the penalties can be severe if you get busted. Just take the high road whenever possible.
The mud-bondage guy