Monkeys are an enemy found only in the Jungle. They're unique among the game's enemies in that they have no way of directly dealing damage to or killing The Spelunker; instead, they steal your items and can stun you, leaving you vulnerable.
Monkeys are generally harmless in that they don't damage the player directly, but they can be a major annoyance and an indirect hazard if not dealt with.
When the Spelunker gets close enough, they will leap from the vines and try to hop onto his back. If they manage to cling to him, after a few seconds he will be stunned and a random item will be removed from his inventory and thrown on the ground. This includes equipment, accessories and treasure. Any held item will also be dropped.
They may also throw objects they find on the ground which can cause damage if they hit you. The player may be put into harms way if he is stunned above a spike pit, or near other hazards such as Tiki Traps or enemies.
If a Monkey does manage to grab a hold of you, it can usually be displaced by jumping repeatedly or performing a flip-hang off a ledge.
Since they only have 1 HP, they aren't too troublesome to deal with, but always try to kill them before they get a hold of you. Long ranged weapons and thrown items are the most effective method of killing them safely.
They can frequently be found on the vines above spike pits, so they usually manage to get themselves killed in the attempt of jumping for you, only to miss and skewer themselves.
Spelunky's monkeys are probably inspired by those in Nethack, who are known for performing weak attacks on adventurers, stealing items, then fleeing.