Ranma 1/2 Is a classic. Its about a martal artist boy named Ranma who's cursed to be a girl every time cold water splashes on him, and Hot water turns him back. On top of that He has at least 3 girls who claim to be his bethrothed and he has an endless stream of rivils and admires for both his girl and boy half combined! Its a very crazy anime!
Ooh bakemonogatari counts... if you don't understand the meanings behind some events, it might confuse you a bit, though. Early in the series, he does end up with one girl, but then that is when the other girls come in, which switches it up a bit.
I tried this thinking there was action, but its mainly 5 girls hitting on one guy at a high school for monsters, you might like it.(note he is a normal human and they are monsters)
Guardian Hearts. Manga's good, not sure how good the show is.
Mahoraho. A classic
Shuffle! Makes sense that a good harem is based off a harem game