Final answer:
The Fanny Pack is the item in 'The Binding of Isaac' that increases the likelihood of dropping pickups when Isaac takes damage.
Step-by-step explanation:
In the game "The Binding of Isaac," the item that increases the likelihood of Isaac dropping pickups such as coins, bombs, or keys upon taking damage is the Fanny Pack. When Isaac is hit while holding the Fanny Pack, there is a chance that he will drop a random pickup, which can be very beneficial during gameplay. The other items listed have different effects that do not influence the drop rate of pickups upon taking damage.