My VW Touareg came with Dunlop Gran Trek tires and I loved them. They handled very well both on road and the little bit of off road driving I do (mostly grassy fields, but some muddy fields). The Gran Treks gripped very well, made the Touareg handle like a much lighter vehicle (it weighs almost 6000#) they were great in the corners, didn't slip in rain or modest snow. Unfortunately they only lasted about 30.000 miles. I recently put on Goodyear TripleTreads and they are very good, not quite up to the handling I got from the Gran Treks but all the reviews suggest I should get longer life out of them.
The only time I ever had a problem off road with the Gran Treks was on a soggy spring day when I tried to pull a trailer out of my side yard. The trailer sank and the Gran Treks just packed up with clay and I got nowhere. Unhooking the trailer allowed me to move the vehicle, and I pulled the trailer out with a tractor. Still, I'd have simply replaced the Gran Treks with another pair if they had given me a longer life.
The wife's Volvo XC90 has a set of Perelli tires on it. They are soccer mom type SUV tires that are great for driving on the road, very very quiet tires, but there is no way I would trust them any farther off road than the front lawn. I'm not sure what she had before this set but they had far more road noise than this set. I am not sure of the model, but for some reason P-Zero comes to mind?
One tire that I had on several previous vehicles that I really liked was the Dunlop Radial Rover. Its a good tire for SUVs and light trucks that spend most of their time on the road but occasionally venture into the dirt, sand, grass. They never let me down.