As far as I'm aware, the United States doesn't issue working holiday visas. However there is the more restrictive J-1 Visa (exchange visa). There are several organisations that operate work exchange programmes but you are usually restricted to prearranged work and you have to organise everything before you leave home.
The most popular exchange programmes let you work on work on a Summer Camp in the States. The work is relatively easy and you can have a lot of fun, but it only lasts about six weeks.
See these sites for more information:
http://www.campamerica.co.uk/
http://www.greatcampjobs.com/
http://www.bunac.org/
If you are a full time student BUNAC's Work America programme may interest you:
http://www.bunac.org/uk/workamerica/
If you want to stay a full year, you should consider working in Canada. Canada has a WHV programme and most major Canadian cities are only a short distance to the United States so you can make lots of weekend trips across the border. Montreal is only a 45 minute drive to Plattsburgh, New York; Niagara Falls in right on the border; Windsor is just a $2.75 local bus ride from Detroit and Vancouver is easily placed for weekend trips to Seattle.