You need permission to use copyrighted material. Period. It doesn't matter if your giving it away, promotional use only, seling the cover art, you need permission. You need permission form the master copyright holder to use the track, and from the publisher to create a physical duplication which is called a mechanical copyright. Without these permissions and or paying royalties you could be sued.
HOWEVER.
The hip-hop industry has a long standing silent agreement that they don't go after mixtapes because they help with the promotion of the music. If you really are just giving your tapes out for free, then the hip-hop industry is not going to bother you. If your selling them, it is still VERY unlikely that they are going to bother you, but you increase your chances.
An example of when the music industry did care: Danger Mouse put out the Gray Album, the famous blend of Jay-Z's Black Album and the Beatles White Album. The album was released for free. Some stores were selling copies they downloaded, but this had nothing to do with Danger Mouse. The hip-hop industry, which is very used to mixtapes didn't care. Jay-Z put out an a cappella version, of course thats what people were going to do with it. However, the Beatles catalog, the publishing rights owned mostly by Michael Jackson, sued. They thought Danger Mouse was making a profit off the Beatles catalog because the CD was being sold in stores. When they found out that he wasn't making money, and didn't have any money, they took other legal recourse. In order to avoid being sued he had to sign over some of his future music earnings as a producer to them. In their mind he became famous by breaking copyright law, and leveraging the Beatles catalog.
The moral of the story is, if you can stay under the radar your probably going to be ok. When you gain national attention, there are going to be some people at the top with their hand out.
