I used to do it on my mountain bike, but I live on the edge of a national forest. My old labrador, and later the shepherd that replaced him, could do six or eight miles easily on flats or uphill. The lab also used to run with us. He could do 10 miles with me, six or so with my wife and cry to go again when we brought him in the house. On one ride, a slow-paced 13-mile climb from our house at 4900 feet to a nearby peak at about 8800, he kept up with us with no trouble at all.
Still, I wouldn't do it on the road, and I'm not sure I'd do it offroad again, either. At the time, the property around us was very sparsely developed, so there was almost no traffic. That's not the case anymore. Downhills are killers, too--the dog tries to keep up, and it can't, so you either have to wait or hope it can find you at the bottom. Water is an issue, because we used to have free-running streams, but they've mostly dried up as development has spread. You'd have to carry dog water for any outing longer than 15 or 20 minutes. If they bolted after a deer or rabbit, as happened a couple of times, there was little danger to them and they could find their way home (the shepherd was gone overnight one time; that's when I stopped letting them run loose). And road riding is an entirely different problem, with cars and distractions and kids and pedestrians who might be bitten. Way more trouble than it's worth, IMO.