Over the years, I've found that a pair of lightweight plastic mountaineering boots work best, something like the Koflach Degre ($255; www.koflachusa.com). They're warm, keep your feet dry, aren't too heavy, and have enough stiffness so that you have good control over the snowshoes on steep terrain or in heavy snow. Asolo's AFS Guide (www.asolo.com) is another excellent boot for this purpose, but these are hard to find. They sell for around $280.
If you do a lot of snowshoeing, and maybe some summer glacier mountaineering, the above are the right amount of boot. If not, then I'd say you need less. The second-best choice is a good, mid-weight leather backpacking boot. Again, you'll need something with a little heft to control the snowshoe. And, you want it to be warm and waterproof. Top of the list would be a boot such as the Montrail Moraine ($230; www.montrail.com). You can use this year-around, for snowshoeing, backpacking, even light mountaineering. The Zamberlan Ladak ($195; www.zamberlan.com) is more flexible and has a Gore-Tex lining for extra waterproofing. Or, try Garmont's Pinnacle ($205; www.garmont.com), another good all-around boot. In all cases, you'll want to add a gaiter to keep snow out of the boot topOutdoor Research's Crocodile ($60; www.outdoorresearch.com) is as essential for snowshoeing as wheels are for cycling.