You cannot use commercial music without permission or compensation. This isn't about Fair Use, that is a very specific concept. There are places where you can find and use music for both commercial and non-commercial videos. Finding free commercial music for videos is hard to find but things have gotten a little easier.
There is an updated music search engine for CCMixter. You can find music designed for commercial use. You can preview the music to see if it works for you. If so, you can download it and make merry.
The musicians in this section of CCMixter have assigned their music as either Sampling+ where you can re-mix and distributed for non-commercial use or a Attribution 3.0 commercial license.
The Attribution 3.0 license means the musician of the work gives permission to use, alter or place it in a commercial production provided there is an acknowledgement of the musician and, if known, where to find him or her. On the music download page you can click a link to get more information about the musician.
When I use this type of music I make a title card at the end of the video giving the name of the artist or the web site where I found the music.
Why Should I Use A Commercial License If I Have A Non-Commercial Video?
You don't have to. There is plenty of music that can be obtained via a non-commercial creative commons license. Here is an increasing problem. If you upload to YouTube or other video services there are often ads that are placed on the video.
If you promised to use the music in a non-commercial video you "might" be in violation with the license if an ad is placed on top of the video, even if you have no control of it.
At this time I do not know of a creative commons musician that went after somebody whose video was played on YouTube and asked for compensation. It could happen.
Reduce the stress in your life. For those things within your control do the right thing. If you have music in your video make sure it is either has a creative commons license, in the public domain or obtain the rights to use the music in your video.