These are generally employed in two situations. Firstly, they make a useful backup for often unreliable henchmen, and generally rely on the victim blundering into them. The second situation is when victims have already been captured, and instead of killing them in cold blood, they are placed in a deathtrap to prolong their suffering, as well as show how devious and cunning the devisor of the trap is.
It should go without saying that attempting the second method usually allows the victim to escape - the movies have shown us that it is far more effective to just shoot someone in the eye socket rather than strap them in the path of a cumbersome laser beam and then leave the room.

More generally, the Death Trap category will apply whenever a certain amount of practical planning has gone into the killing. The trap need not be a Rube Goldberg masterpiece, indeed some of the most effective traps are the most simple.