Exercising really hard is certainly one way to work up a sweat, but I believe that sweating in general is amazing. When you're in a sauna, steam room, or hot tub (my personal favorite) and your body gets to that elevated heat level, it releases emotional pain from your body. Of course, it also helps with physical aches and pains and the stiff muscles that result from a stressful lifestyle.
I don't believe it's by chance that so many cultures have some kind of "sweat bath" tradition: from hammams ("Turkish baths") to sweat lodges, people all around the world and all throughout time have enjoyed the benefits of steaming toxins from the skin. Ayurveda—the ancient Indian healing tradition—alone uses 13 ways to make you sweat!
Just be sure to stay hydrated when you practice this stress buster; that is, drink plenty of water to replace what you're losing. If exercise gives you shortness of breath or chest pains, then stay away from excessive heat sources. I also recommend that you avoid the Scandinavian practice of going from heat to a cold shower. In addition, pregnant women should forgo saunas, steam rooms, and hot tubs, especially in their first trimester.
Beauty bonus: Steam is a basic component of a facial because it opens your pores and helps with cleansing. Heat also relaxes blood vessels and improves circulation.