I used to work for Carmax a long time ago when I was in college, but I still know a few people that work there and things haven't changed much since then. At least process wise, but the quality of their cars has gone way down due to the sheer volume that they sell now.
They are pretty picky about what they want. Like Mike mentioned, they want a car with no prior body damage. Bumper sprays are ok, anything else will mean your car goes to their wholesale auction. You will get either of two offers, one that is about $1000 less than KBB trade (unless they REALLY want your car because they need them, yes they keep track of particular cars in special demand for that time of year) or they will lowball you really bad.
The lowball is a polite way of saying they do not want your car, but for that offer they will take it and sell it at their wholesale auction.
Its all free so, its usually worth your time to know where you stand. Most autopians will do really well compared to other dealers REAL tradin values (sure they can fudge them to look like you are getting a great trade, but look at the overall price). I've had a few offers that I know I couldn't have done as well in a private party sale. I usually go for the heck of it, let them appraise my car while I take a few test drives to pass the time.