The Hogyoku (Bleach) can manifest the user's desires based on the strength of the user's Reishi.
Shenron (Dragon Ball) can grant one wish (later three) of anyone who gathers the seven Dragon Balls, under certain limitations.
Porunga (Dragon Ball Z) can grant three wishes of anyone who gathers the seven Namekian Dragon Balls, and have been powered up to exceed its former limitations.
Ultimate Shenron (Dragon Ball GT) can grant one wish of anyone who gathers the seven Black Star Dragon Balls, and is so powerful that it seems little to no limitations exists for it.
Super Shenron (Dragon Ball Super) is the omnipotent dragon who comes from the Super Dragon Balls and can grant any wish at all no matter what it is.
After a person fulfills Alluka Zoldyck’s (Hunter X Hunter) 3 requests, Nanika will grant one wish.
Kyubey (Puella Magi Madoka Magica) can grant wishes in the form of contracts which result in the wisher becoming a Mahou Shoujo. Unfortunately, these wishes usually backfire in ways that drive the wisher to despair.
Brew (Soul Eater) can manifest the user's desires based on the strength of the user's soul wavelength.
Jirachi (Pokémon) can grant any wish to anyone! Even if the wish is…
Crossroad demons (Supernatural) can grant the wishes of humans, but said wishes always result in the demon claiming said human's soul.
Vengeance demons (Buffy the Vampire Slayer) grant vengeance-related wishes of anyone who says them, though said wishes often result in the victim's gruesome death or even the creation of alternate realities.
Neil, and later his dog Dennis (Absolutely Anything), temporarily gained the "galactic power", allowing them to fulfill any wish they speak, although the power is quite pedant wording-wise.