Only if you have
FULL WRITTEN PERMISSION from whomever "OWNS" the music.
NOTE that just because an artist performed a song, doesn't mean they are allowed to give it away.
You may have to jump through hoops dealing with management, record labels and others giving you the run around.
There are many "royalty free" sites on the net.
Some you have to pay per use.
Some you are granted an expiring license.
Some you can buy a CD or download and use them over and over.
And some are totally free!
I would personally suggest finding an unsigned band, or hitting up YouTube original music producers and try to collaborate with them.
Sometimes you might have to pay, and sometimes they might just give you Synchronization Rights for some mutual promo.
It's a great way to grow from each other.
There is a section for collaborations on this forum for that as well:
http://yttalk.com/forums/collaborations.42/
Also remember, the bigger you get the more people will want to work with you! So keep it professional and on your best behavior.
Good luck!
**Edit:
P.S. I just saw the posts about using the music for Parody. This is fine, but ONLY under very strict circumstances. Make sure you fully understand Copyright law before proceeding.
Take Weird Al Yankovic for example...he did that all the time.
Depending on what you plan on using, you still might want to get permission. Lawsuits and YouTube strikes are no bueno. Especially since YouTube can just take down your video no matter what....and they don't really care to hear you explain.
yep.