Aa! Megami-sama! (TV), Kono Subarashii Sekai ni Shukufuku wo! Recommendations
Both series have a comedy driven plot starting off with a goddess telling the protagonist they can carry out a single wish. The protagonists then decide to ask the Goddess to stay with them, leaving her in disbelief. Once the goddess joins the protagonist their power is reduced significantly forcing the goddess to adapt to her new environment.
However, whilst in Aa! Megami-sama! the protagonist continuous to live in the same world and the Goddess is please to stay by his side. In contrast in Kono Subarashi the protagonist is taken to an alternate fantasy universe and the goddess considers the protagonist a useless otaku
A Goddess appears in both anime asking the protagonist to make a wish.