Maxxis Bighorns
A 6-ply radial with nice lugs that will get you through anything.
No damage to lawns.
Work well in snow.
I've also heard good things about Mud-Lites if you want to check out a couple options. Go here and do a search for Maxxis and you'll see some info on both tires (as well as others).
I've been very happy with my Essex Surefoot tires, six ply, Kevlar belted, run flat. They have run over cactus, mesquite, rock, mud and who know what else.