A lot of single-camera operators use in-ear headphones, like Mark W. suggested. It lets you know that something is being recorded. You should always have some sort of sound monitoring, the in-ear set or a "proper" pair.
When it comes to "monitoring" the quality of the recorded sound, then yup, the type of headphone is very important. A pair of closed-back cans are essential. There are two main types which are accepted as "standard" for location recording, the Sennheiser HD25 and the Beyerdynamic DT 250

http://www.sennheiser.co.uk/uk/icm.n...76?Open&print=

http://www.beyerdynamic.com/cms/Head...ctdatabase_pi1

Both cost around the £100 mark. I've got the Beyers and love 'em, others swear by the Sennheisers.