Are we talking about without stopping, or in one day, one one road trip...?
Without stopping I've driven from the Nurburgring to Calais, which (by the route I took) was about 325 miles (and one tank of fuel!).
In one day I've driven from Milton Keynes to Edinburgh and back, which is about 700 miles I think all together, but I've taken at least one break on the way there and one on the way back too.
I fairly regularly drive around 1,000 miles in a week, and have done as much as 1,700 miles in a week once or twice as well.