Nets can be used in the off-hand or main hand to snag enemies, even hostile mobs, and pull them towards the direction the player moves, allowing players to drag an enemy while moving backwards, or drag them over the edge of a ravine.
Suggested recipe: 5 leads in 3x3 grid (one lead in each corner, one in center.)
Other people have suggested fishing nets. This could be included as a feature. If multiple small mobs are in the same target area, for example fish in a school, several can be caught at once. Or, if a small mob is already caught, using a net on another small mob has a chance of catching both. There should of course be a limit, probably 3 or 4 small passive mobs or 1 neutral/hostile mob.
This is not meant to be like the capture nets that appear in some mods, which pick up mobs to allow for easy transport similar to a fish bucket. It's more like a special kind of lead that works on hostile mobs. Also, it makes Roman-style net and trident gladiators possible in Minecraft.