Let me start out by saying that Ah My Goddess is one of my favorite anime - both the OAVs and the excellent movie - so I strongly encourage everyone to at least rent if not buy this one. Ah My Goddess originally started out as a manga by Fujishima Kousuki, and having not read the manga, I can't comment on how closely the very short anime series follows it.
The OAV begins with a boy named Keiichi who decides to order food one day and accidentally dials the Goddess hotline. To his surprise, Goddess Belldandy appears and offers to grant him any wish. Keiichi immediately believes his sempai is playing a joke on him and off the top of his head wishes that a girl like Belldandy would be with him forever. After a brief consultation with the heavens, Belldandy tells him his wish has been granted. And thus begins the start of Keiichi's new life.
Almost immediately, sempai returns, and seeing that Keiichi has broken the No Girls Allowed rule of the dorm, tosses them out on to the street to find a new home. But as Belldandy is the Ultimate Girlfriend, she is quickly able to petition the powers that be to find them a new home in an old temple nearby. Yes, she cooks. She cleans. She has magical powers. She can heal. She can make the best of any situation. And she is perfectly content giving up her Goddess home to live with Keiichi. Life is perfect for Keiichi... until his sister, Megumi, shows up... and then Belldandy's two sisters show up... and everyone lives together in the temple.
Keiichi deals with Megumi pretty well, especially when she offers him her stipend to get buy with. Belldandy's older sister, Urd, however, is another matter. She immediately shows up and tactfully encourages Keiichi to make a move on Belldandy... something he's not at all comfortable doing because, well, he's never had a girlfriend before. And of course someone or something always seems to get in the way. Not long afterwards, Belldandy's jealous little sister, Skuld, appears and tries to break the two up so Belldandy will be able to return home.
In all honesty, the animation in AMG isn't as spectacular as it could have been. And there are points where the drawing style changes dramatically throughout an episode. Those minor differences, however, don't detract from the quality of the anime. They also seem to have gotten a bigger budget for the last 2 episodes. The music to AMG is superb and greatly enhances the anime's overall themes of love and sincerity with its lyrics and melodic instrumentals.
The allure of Ah My Goddess lies in the absolute sincerity and honesty that all of its characters possess. Imagine the situation - a boy half heartedly makes a wish and a second later, he and a girl he doesn't know are contractually bound together forever. Sure, you've most likely seen the basic premise before - girl meets boy and then the two live together in a house full of girls that share an interest in the relationship - but Ah My Goddess is unique in the heart warming sincerity and openness that each of its characters possess. And the focus is on the positive instead every obsessive detail that most comedic romances use as slapstick. The story that ensues follows them as they work through the details of being a couple and falling in love.