The whole "harem" genre thing is a bit vague, imo. Like, I've heard people describe the Clannad as "harem" because it's basically one guy and a whole bunch of chicks who fall for him at some point. To me, "harem" anime means a character generally ends up being sexual with a bunch of different people. I don't know any like that, but yeah, there are lots of romance style animes out there with multiple romance interests going on.
Toradora is amazing. High school romance/drama type stuff. Really made a big impact on me.
Clannad. Prepare yourself for all the crying if you watch this. ;-; Me and my friend were actually tearing up within 10 episodes when we watched it. My mum full-on cried watching it with my brother.
Daily Lives of High School Boys (Danshi Kōkōsei no Nichijō) is amusing, at least to me, so that's a comedy suggestion.
"Fantasy" describes a whooolllee tonne of anime. I'm assuming you don't mean shounen stuff (Bleach, Naruto, etc.) but rather just anime with fantastical elements.
Gurren Lagann, Full Metal Alchemist: Brotherhood (WATCH THIS NO MATTER WHAT YOUR PREFERENCES ARE), and Shingeki No Kyojin (SAME GOES FOR THIS) are all awesome and fall into this genre for me. I don't really classify them as shounen because they're a lot more mature in their content and are enjoyable for anyone, not just young males.
A couple more great anime are:
Stein's;Gate (time travel paradoxes, plot twists, and amazing character development = amazesauce);
Kill la Kill - which I didn't include above because it's a wee bit shounen-ish due to fanservice (although it mocks itself for this so y'know);
Black Lagoon (this gets dark as fuck about halfway through but it's still good);
and Death Note (supernatural elements but is mainly a thriller.)
Redline and Stranger: Mukou Hadan are some good anime films, particularly the latter.