I have some people that request to do that... basically, you have the mic you can sing the lyrics on the screen, parody lyrics, or freestyle.
It's only a few that request it and I've seen one or two people that are really quite good. The trick is to make sure they only do it for a short period of time. I also make them pick what they want for backing themselves so they don't yell at me when the rest of the 'crew' on the backing track start in. If you want to get a break, the crowd doesn't mind and don't know what to use, I recommend rapper's delight - it's 7 minutes long, no background vocals, and a basic hip-hop beat. If they want something faster you can look for baby got back, bust a move, or to really mess with them throw in Ice Ice baby...
BTW, many of the eminime tracks are pretty easy to freestyle to.
Remember, keep it short enough they don't disrupt the show, and pick beats already in your book. I don't let them bring their own - I'm doing a karaoke show, not a hip-hop battle. You do have to be careful about a group getting up and passing the mics around though because they think they're 'better'....