Every once in a while. We have a lot of nicknames though I suppose. Though I hardly ever use his actual name when we are at home. Unless he is in trouble.
Every once in a while, DH will call me babe. He usually uses the nickname I've had since childhood that only about 5 people use. I'm not a "term of endearment" kinda gal. It caused some friction when we were first dating because he was a real "baby, sweetly, darlin" type guy. I call him by his first name, unless I'm feeling snarky. Then I call him sweetheart, dripping with sarcasm.
Um.... we do. It's a force of habit. I more often call him by his nickname and a couple other terms of endearment, but babe/baby is in the regular rotation. He also calls me babe. I also call my babies babe.