Without cheats, because I don't believe in them, I did a 5:17:778 lap on Nurburgring in the Audi R8 Race Car '01. No crashes, though I did hit the grass on a couple of slight bends and a couple of straights. The only thing I did to the car was used the "toolbox" to bump up the power, lower the weight, and max the top speed, but all of those are built into the game.
Top speed on the run was 243 on the long straight by the real entrance and exit of the track.
Now for some real fun, I actually got to drive the track while on a mission trip in Germany in 2012. One lap in a 6-speed, 4-cyl Ford Mondeo rental. It was slow, but it was AMAZING! If you ever get the chance, it's only like $28 USD to buy a single lap ring card. Go for it!