Yes, it is illegal.
Your iTunes/Napster/Rhapsody/Tape/CD/Album license basically allows you to use the copy for your own personal use.
You can of course arrange a separate license agreement with the publisher or artist/composer rep group suck as ASCAP, BMI, SESAC, SOUNDEXCHANGE etc. In those cases you will probably have to pay a flat fee or per copy royalty for each game copy you release.
Will you get caught? Probably not. Will you get sued? Probably not. Look at all the IP and Copyright violaions on YouTube MySpace etc.
If you do and get caught, be preapared to pay out a settlement to RIAA or be willing to go to court and spend thousands on a lawyer.
Your best bet?
Go with Royalty Free music like Daz and others offer or use Creative Commons released tracks (podsafeaudio.com is one place) that you can use for a low flat fee or no cost at all like stuff I create.