I've been dealing with my long nails without nail clippers ever since I was a child.

Start picking at one edge of the nail (the side closest to the thumb). You will soon get a small split. Pull on this nail edge and the nail will tear. It follows the grain which curves around the end of your finger so you don't end up tearing your skin.

It works great and you can do it on your toenails too.

Although now that I am an adult, I use clippers so they look neat.

They probably were worn down from the daily physical labor they had to do.

Probably the same as with today's pet dogs - we have to cut their nails, b/c they don't walk anymore enough to file them automatically.

I wouldn't be surprised if after breaking off a piece one would file it a bit on a rock or so, or bit off whatever is annoying. Hard work would take care of most of the issues :)

My nails grow like crazy. I use my hands a lot every day and my nails have never been 'worn down' by any activity. They will get long, and then will start getting in my way, and then getting chipped, which means they snag and scratch and are a PITA. They require plenty of maintenance to keep them functional and comfortable. Longer nails are a useful tool for many tasks.

A lot of animals perform some sort of self-care to keep them manageable and functional. I have read that chimpanzees and other apes frequently bite their nails to keep them useful. My cats not only scratch to shed the outer sheath of their nails, but often bite them off. My pet rats kept their nails trimmed by biting them.

Animals who run long distances in their natural environment, like dogs, don't have these behaviors of course.

Dunno myself, but here is some mildly interesting speculation from another site:

http://ask.metafilter.com/131168/outgrown-nails

They could certainly bite their nails and chew them off.

I don't think they would just wear down. I have often cut my nails with a knife when out in the wild for extended periods. My guess would be they used something similar. Like a stone knife, rasp, or just teeth. It's true that some wear and tear would take place but from my experience with stone age technologies (not for paleo sake) it wouldn't be enough. As for toenails as someone who doesn't wear shoes when not in the city. I can say being barefoot doesn't keep toenails short only dirty.