There's a wide array of choices when it comes to renting a car in Germany, and, if you're prepare to pony up some hard-core Euro, there are rentals for people who love to drive. Unfortunately, even though the Nurburgring is billed as a public toll road, driving your rental on the 'Ring is a nebulous matter these days. Many rental car companies have written clauses into there rental agreement excluding the 'Ring from LDW coverage. And the ones that aren't, really don't specify how they deal with accidents. As tempting as it was, it was clear that our SixT Audi A5 would not be clocking 9 minute laps with me behind the wheel.
After much research, we decided to rent a race prepped E92 325Ci from http://www.rent-racecare.de and the experience was nothing short of fantastic. The morning of our arrival, we were greeted and escorted to the track by Theo Kleen, the owner. Knowing my complete lack of real world experience, he offered up an instructional lap in his MK5 GTI with my wife and I as passengers. Theo has logged over 4000+ laps and he chatted away happily with us while he went through the track at speeds that made my (later) laps look painfully slow (they were). After completing the lap, he tossed me the keys to the E92 and wished me luck. The car ran flawlessly through all 8 laps and even though I exceeded my mileage limit, Theo was less than exact about charging me overage fees. If the 325Ci seems a little sedate by your standards, Theo's stable also includes an E92 M3, E36 M3, 135i, and Porsche Cayman.