Hi Jess –
You are not allowed (legally) to use copyrighted music for video – Whether that be posted on the web (YouTube, Vimeo, etc….) or even for your own use (although I doubt anyone will ocme into your house and check all your home videos).
You need certain licenses – such as sync, mechanical, performance, distribution, etc… – to use this music in a video production. Some copyright owners are more lenient but most do not give up these rights easily or cheaply. In other discussions I have had over the past few years I have been told astronomical sums are required to secure these rights unless you are a movide studio, TV station, etc…
To solve this problem, those who choose to stay on the side of legality use what is called royalty free music – You purchase the rights to use this music in other productions, such as video. Some of this is very expensive and some is very reasonable – and you’ll find both great and crappy music at both extremes and everywhere in between.
The legal issue is not a trivial one and the Digital Millenium Copyright Act has very sharp teeth that can impose very large fines on those who break it’s rules.
Do a search on royalty free music, also known as buyout music, here on the forums and you’ll see many options available to you.
This is a very simplistic answer and if you’d like more details or examples, please ask.
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