Among climbers, Mount Fairweather holds the unofficial distinction of the worst-named mountain on earth. The peak is lashed by near-constant snowstorms, and even getting a good view of its icy form is notoriously difficult. When explorer James Cook gave the peak it's name in 1778, he was offshore during a rare period of clear skies.
By any measure, Fairweather is one of the world's major summits. It is the third most prominent peak in the United States (after McKinley and Rainier), as well as the highest and most prominent peak in the large, extremely mountainous expanse of British Columbia. Rising almost directly out of the ocean, it contends with nearby Mount Saint Elias for the title of highest coastal mountain on earth.
The major obstacle to an ascent of Fairweather is, of course, the weather. These days, aircraft are permitted to land at an elevation of about 9,000 feet near the Grand Plateau Glacier, allowing a relatively quick ascent via the West Ridge if you are lucky and get a settled high-pressure cell. However, many purists might question starting this high--it is roughly analagous to climbing McKinley by flying in to the 14,000-foot camp, or Rainier by flying in to Camp Muir.
It is quite possible to climb Fairweather from sea level during an expedition of a few weeks or so, so flying in to high camp robs you of an opportunity for a unique sea-to-summit experience. Still, given its remoteness and bad weather, any ascent of this peak is a significant achievement no matter where the climb starts. At most, only several parties a year attempt it.