Yes, there are a couple of products available that "claim" to remove vocals, but there is a catch. They can only really do it if the vocals are center panned and at exactly the same level on both left and right channels. If you really want to add your voice to popular songs, you may wish to consider going to http://www.karaoke-version.com/custombackingtrack/ and seeing if the songs you wish to record are there. The music is usually very close to the original artist, and you can choose how to mix the version you download. Prices are reasonable, but the only problem is that they cannot be used for commercial purposes without specific permission. You can choose the key that you want the music to be in, remove instruments if you want, leave or delete background vocals, etc. Overall this is not your average "karaoke" site. High quality sound and very flexible. Check it out.
I agree with Procyon that you could use the "Karaoke" effect, but that will really only minimize the vocal track, not eliminate it in most cases. Which means that your vocal could be louder than the original which has been minimized, however if you are not singing in the exact same key as the original vocalist, it is going to sound very strange and likely out of key.