These companies offer a variety of services, with some providing a full spectrum of weather information and others targeting a particular audience such as boaters or pilots.
Colorado State University's Tropical Meteorological Project, the group headed by Dr. William Gray that began forecasting ahead of the hurricane season in 1984: http://hurricane.atmos.colostate.edu/Forecasts/
Britain's Tropical Storm Risk, a group funded by the reinsurance industry to keep losses at a minimum. TSR produced the most accurate long-range forecast for the 2005 hurricane season: http://tsr.mssl.ucl.ac.uk/
Hurricane Alley, founded by Tom Berg, a self-taught climate expert, whose landfall and seasonal predictions have gained respect in the climate research community and a following among weather watchers: www.hurricanealley.net/seasonal.htm General information
NOAA Atlantic Basin