Downhill Mountain Bike Shoes
Downhill mountain bike shoes should be a match for the terrain they are intended to cover. Just like hiking boots, downhill mountain bike shoes should be made of durable materials - leather and rubber, in particular - and should be substantial enough to protect the foot from sharp rocks or pointy branches should a collision occur. Thick, chunky treads, or soles, are important for ease when walking in the woods - you will be pushing or carrying your mountain bike at some point during yuor ride, and will need the proper traction to ensure you do no let your feet fly out from under you.
Should you opt for a clipless pedal and shoe system, it is important to purchase a shoe with cleats that are recessed into the sole enough to allow your sole to have enough traction on the ground. If specifically using the shoes for mountain biking, it is also important to purchase a two-bolt cleat instead of a three bolt, road bike cleat. The smaller cleat allows for more surface area of the shoe to grasp the ground when walking.
Shoes should also be supportive, providing enough of an arch to maintain comfort while downhill mountain biking. They should be snug, though, and firmly cushion your foot so as to prevent slippage and injuries. Adidas, Sidi, and Shimano are companies who are known for their high quality downhill mountain biking shoes.