If I was to be brutally honest I would say most Animes people have praised. Not trying to be especially cynical here, but the japanese animation industry, at least now, isn't exactly the paradigm of creative freedom.
Right, now before I have my ass chewed off, read what follows... I completely understand the draw to anime. They offer a wealth of themes, atmospheres and characters that most western animations won't touch due to their kid friendly production ethos. But I think most of this wealth only works as a novelty. Too few of the Animes I've seen (and I'm still watching animes to date) have actually made anything other then an aesthetic or narrative gimmick... they all fall into derivative plot twists or cookie cutter story arcs, conceptually great characters become angsty parodies of themselves (usually once their motivations have been revealed) making some of the more emotionally charge shows unbearable when their drive is something petty or shallow or ludicrously overwrought.
Oh and don't get me started on the stereotypical characters they like to stuff haphazardly into every god damn show. Nothing like a shallow piece of eyecandy or painfully whiney protagonist to completely detract from a weighty plot line or completely crap on a emotional sequence for simply being there.
I watched anime for years, following all 3 of the still running juggernauts (One Piece, Bleach and Naruto) and a few of the earlier ones like Dragon Ball. I've watched anime of completely different styles, qualities and even targeted demographics. From Sailor Moon to Ergo Proxy, Elfin Lied to Toradora and possibly hundreds more of equally distinctive shows.
Don't get me wrong, some of my all time favourite pieces of media have come from Anime... not all of them do what I said above. But a lot do to some degree and there are other issues which I haven't touched on. I have also done quite a bit of research on the Anime industry and there are things I learned that have jaded my enthusiasm towards it...
I just can't take a favorable stance towards Anime anymore.