I bunny proofed one room and watched ours when out in the rest of the house. We were lucky and never had a problem. I know some rabbits just chew or dig more than others and younger rabbits can be worse than older rabbits. Ours were content with lots of hay, in several varieties, freshly cut unsprayed apple branches and untreated willow baskets. We also fed some fresh foods every day. I guess an old table leg didn't look all that tasty. Like I said, we were lucky!
There are several different types of things available for covering cords. You can block off some areas or surround a particular piece of furniture with boards, too.