In my opinion, a good anime is one that gets you thinking even after the credits of the last episode roll. Or even better, after each episode. For example, a select few animes like Clannad, Madoka, and School Days got me thinking for the rest of the day about what happened and I even analyzed the characters, plot elements, conflicts, etc. in my head. In Clannad's case, I actually longed for more episodes (even though the story was essentially over) so much that I entered emo mode for about a week aka dark times in my life xD
Dramatic elements in the plot will always be #1 in an anime. An anime like K-ON! is fine for entertainment, but only dramas can really give me the effect of "this is why I watch anime". Also, fanservice can make or break an anime; It can add to the "enjoyment factor" as long as it isn't present every fucking five seconds and comedy is nice because it just adds some lightheartedness amidst all the drama. For me, animation quality is extremely important (for better or worse) because an anime with bad art is just hard to watch. This can be bad though, because I rarely watch pre-2005 animes due to difference in animation quality. OP and ED can really contribute how the anime affects me in the long term, a memorable OP will remind me of how good/bad the actual show was but is just a nice addition.
Also:
Seinen > Shoujo > Shounen.
TL;DR:
Has to be memorable, have a good (dramatic) plot, a little fanservice, comedy, decent animation.
Dramatic elements in the plot will always be #1 in an anime. An anime like K-ON! is fine for entertainment, but only dramas can really give me the effect of "this is why I watch anime". Also, fanservice can make or break an anime; It can add to the "enjoyment factor" as long as it isn't present every fucking five seconds and comedy is nice because it just adds some lightheartedness amidst all the drama. For me, animation quality is extremely important (for better or worse) because an anime with bad art is just hard to watch. This can be bad though, because I rarely watch pre-2005 animes due to difference in animation quality. OP and ED can really contribute how the anime affects me in the long term, a memorable OP will remind me of how good/bad the actual show was but is just a nice addition.
Also:
Seinen > Shoujo > Shounen.
TL;DR:
Has to be memorable, have a good (dramatic) plot, a little fanservice, comedy, decent animation.