Personally I dislike most harem anime especially if they fall into the trope of:
a) Violence against men is cute! I hit you because I'm jealous! Aren't I Kawaii! ^.^
or
b) JDPS (Japanese dickless protagonist syndrome)
If you are a late teenage boy, or young man, surrounded by beautiful women who would do anything for you, you literally can not mess up, and all you can do is get embarrassed around them, then you might have JDPS. I guarantee any real male who isn't either inhibited by religion or not attracted to women would dive into at least one girl head first. It's unrealistic.
There is a reason that JDPS exists, and it has to do with men in modern Japanese society and I don't feel like getting into that right now.
I will say though that the Japanese guys who like harem anime I've met in RL are some of the creepiest people you'll ever meet, and these are the people that these kind of anime are aimed at.
That being said, it is possible to do it well. Highschool DXD has a more realistic male protagonist at the expense of realism in the women, but the story with the angels, devils and fallen angels is rather interesting, even if the producer has said that the main character "will never have sex with one of the girls because if he does that once, that's all he'd ever do"
I also have a soft spot for Zero no Tsukaima, due to it's world building, although it does fall prey a bit, especially toward the beginning, of violence being cute.
Also any anime with nosebleed spurts is immediately stamped with a giant F.
Dishonourable mention goes to Rito in To love-ru. Dude is the epitome of JDPS, even if I do think most of the girls in the anime are great, Momo in particular.