An anime has to be well-thought out for me to enjoy it. I generally like stuff with an engrossing plot, and a tone that isn't too silly. There are exceptions though, to everything. Something recurring to me has been how women are portrayed in anime; I generally like anime where the women are strong, intelligent characters, whether their alignment is good or bad. I also really value imagination in anime. If it's too heavily reliant on tropes and cliches of any given genre, it won't appeal to me really.
Another kind of anime I like is one which appears to be not-so-serious on the surface but has a lot of subtext and meaning underneath if you look carefully.
Strong female roles is another reason I like Anime.
Even though I like Ah! My Goddess
Is it only me that when Belldandy acts like a perfect little housewife and it kind of bugs me. I don't know exactly why. I think it's the fact that keichi is letting her cook and not helping out. he'll be in his room watching TV or something.
I dunno, I have a pet peeve when dudes don't help out the significant other around the house.
Yeah, I hear you. Ah! My Goddess! is a hysterical show though, and I actually really like it despite its tropes of perfect-shufu harem character (Belldandy) and hopeless (yet sensitive) guy (Keichi). I own the DVDs either way. The first time I saw it, I literally laughed so hard I woke everyone in the house at about 2AM. Another show that has similar elements (in how you were mentioning Belldandy's character) is Fruits Basket. I actually kind of hate Toru Honda, but at the same time, find her cute, to the point I've convinced a friend of mine to cosplay her with me (her as Toru, me as Hanajima). It's also one of those shows I make an exception for.
I guess generally speaking, unless there's some outstanding circumstances, I don't like anime with stereotypical gender roles, or at least not hypermasculine/hyperfeminine ones.