Do you have to cut dogs' nails?

I find it hard to believe that there isn't a natural way to avoid dogs' nails growing unhealthily long. If they were wild, they wouldn't run around with claws so overgrown they couldn't walk straight. What do wolves do? Do the claws just wear down, naturally, as they run around and dig? Do I have to cut my dog's nails or can I just take her for a good run every day to keep them short? Would the pavement wear them down?