We clip our cat's claws. When we don't keep up with it on a regular basis, the claws often get so long that they catch in fabric and the cat cannot move, struggling and getting all hysterical! So it's best to keep them trimmed. Our DSH does a pretty good job on chewing at his claws to keep them trimmed, plus he uses the scratching posts pretty regularly (also the stairs! Grrr! ) The Tonkinese has more trouble with his claws, or maybe I just notice it more because he's always on my lap and he sleeps under the covers with me at night against my bum, so I FEEL those sharp claws! I have to keep his claws trimmed or I pay the consequences! And, yes, we still have some ruined leather furniture and stuff from their claws. Also, our cats are not allowed outdoors. It's safer & healthier to keep your cat indoors.
Here's a link on trimming claws: http://www.vetmed.wsu.edu/ClientED/cat_claws.aspx