Most artists or bands already have some cover songs that they like and play anyway, so why not do a cover version? The major reason that most artists shy away is the licensing issue. You want to be able to pay the songwriter for the song as you're legally bound to, but most artists have no idea where to start.
Now comes a service from a company called Rightsflow called their "Limelight" service that will do just that. For a flat fee, Limelight will do the research to find out who the songwriter and publisher is (in case you already don't have that info), and will work out a licensing deal based on the manner that you'll release the song (CD or digital download, for instance).
Another benefit from using Limelight is the fact that you prepay the license so you don't have to worry about keeping track of sales and report back to the publisher, which can be a major pain.
Just a little aside - if you do decide to release a cover tune, make sure you get your metadata together. The reason why your doing this in the first place is so people will find you, so you have to optimize your chances by optimizing your keywords (as I discussed in many other posts) and making sure that you supply all the pertinent MP3 data as I discussed here a few days ago.
This is a quick and easy way to work out a licensing deal for a cover song, but if you have any legal questions, be sure to check with a qualified music attorney.
Don't forget to check out my Music 3.0 blog for tips and tricks on navigating the music business.