Headphones are certainly one accessory that no studio can afford to be without. They're vital, in particular, for recording vocals, as they enable you to hear the music without having your monitors (speakers) turned up.
You can now pick up a pair of studio-standard headphones on a home recording budget, so there's really no excuse not to get yourself a decent pair. A closed-back design will work best, as they enclose your ears, resulting in the minimum amount of spill (noise picked up by the microphone) whilst having them turned up nice and loud.