Leakage is the prime consideration for headphones used for tracking or overdubs. Studio microphones are noted for their dynamic range -- capturing both loud and quiet sounds. Headphones come in two basic designs, open- and closed-back. For purposes of recording vocals, only closed-back designs are suitable, but even then, some headphones work better than others. Models such as Audio-Technica's ATH-M40 and ATH-M50, Beyerdynamic's DT770 and Sennheiser's HD251-II Pro are good for monitoring while recording.
The frame of mind of a performer is something that should be considered to achieve the best results. If you are putting vocals on a quick demo, the feel of a pair of headphones isn't a big factor. However, if your session is several hours long, uncomfortable headphones can be a nuisance that may influence the performance. Headphones such as Shure's SRH840 and Ultrasone's Pro 900 are known for their comfortable fit, making them excellent choices for extended sessions.
Home studios are noted for making equipment multitask. This means that headphones used for vocal recording may also be pressed into service to do some mixing when other members of the family are sleeping. In that case, sound quality becomes a priority, whereas accuracy is not as important when tracking or overdubbing. Sony's MDR7509 and the Beyerdynamic DT250 provide good sound quality in a closed-back design.
Headphones are available with different cable designs -- single or Y cables, straight or coiled -- and each has advantages. Some manufacturers, such as Fostex, have detachable cables. These are handy for replacement as headphones can take a beating and usually the cable fails first. For singers who like to hear their own voices, single-cup headphones like the Beyerdynamic DT252 are a useful option because there is no unused cup bleeding sound into the microphone.