I count five distinct varieties up to now, not all of whom have made it into the TV series..
Ice zombies - Wights, malevolent reanimated corpses, controlled by The Others.
Fire zombies - Beric Dondarrion, Lady Stone Heart, possibly Melisandre - Reanimated people who retain some or most of their human characteristics, depending on how many times they've been reanimated, and their physical condition as it is performed. This is accomplished by certain followers of the Red God, R'hllor, by means of its power. UPDATE - As this reddit comment points out, Beric and LSH are probably resurrected, rather than merely reanimated. Clearly, they are quite different from the other types listed here.
Bloodraven zombie - Coldhands an apparently intelligent and benign character who is vital in Bran's journey to meet the Three-Eyed-Crow.
Frankenzombie - Gregor Clegane, aka The Mountain, reanimated as Robert Strong by Qyburn.
Further, it's close to certain that Jon Snow - unless he somehow survived the attack by his murderous Night Watch brothers* - will be brought back, possibly by Melisandre, though perhaps by some other agent. Bloodraven is a possibility, but I think Val, the Wilding Princess, whose grey eyes mysteriously turned blue, might have a part to play as well.
Did I miss any?