I don't know if you can say that the Fall of Constantinople in particular had any direct effect, but the rise of Ottoman Turkish dominance in the near east, the decline of Mongol power, and the consequent increasing arduousness of old Silk Road routes in the spice trade was certain a factor in motivating attempts to find alternate spice trading routes (around the cape of Africa, or straight west).

A bit more speculative, but it's also possible that the fall of Constantinople, and thus the fall of Genoese commercial interests in Constantinople (which were very significant) lead to Genoese men like Christopher Columbus looking further afield for opportunities. In a scenario in which Constantinople never fell, perhaps Columbus would have been too busy with some venture in Galata to try a westward voyage. That's very speculative, though.