Captain James Cook bestowed this 15,300-foot peak with one of the most ill-fitting names on Earth. Mount Fairweather, which straddles Alaska and British Columbia, overlooking Glacier Bay National Park, receives an average of 100 inches of precipitation per year. For mountaineers, climbing Fairweather is as out there as it gets in North America. That’s why Alaska Mountain Guides, which has a perfect safety record, with no major incidents or accidents in over 20 years, requires that its climbers have a solid résumé, including ice-ax proficiency and mountaineering experience in the region. To be sure, this is a tough trip. But it’s worth it: you’re climbing 7,000 feet while overlooking a massive ice cap and some of the most spectacular fjords on Earth. $4,900.