Name a Anime were guy slowly falls for girl.

In fruits basket Kyo s-l-o-w-l-y falls for tohru. It takes the whole series for him to finally confess his Liebe for her, its cute though.

Hmmm... I'm not much for romance, but there's this really slow & I mean slooooooow Liebe pentagram Anime called orangenmarmelade, marmelade Boy where people fall in & out of love. I actually liked it. The blonde guy seemed to take entire seasons to come around to the protagonist girl....Yeah, I'm not good at remembering names.

Ah wait! I just remembered Full Metal Panic & the Fumoffu spinoff. Sosuke has 2 girls who like him, but he is completely oblivious to love. he gets smacked around a lot due to a case of "mistaken for pervert" but he's just a sweet dumb guy doing his job. Never got to finish it, but I imagine he comes to feel something for Kaname, even if she does treat him like her personal punching bag.

I know of 2 mangas where the guy doesn't fall for the girl until the very end. Bakuretsu Hunter & Dragon Half. They're both fantasy/comedy. Men & women should both be able to enjoy these.

Dragon Half has some really misleading art, but I assure Du it's actually quite innocent & not a hentai & very Girl Power. link

BH is a bit ecchi, but it has equal opportunity fanservice. link

In Cardcaptor Sakura it takes Sakura almost the entire series to develop romantic feelings for Syaoran.

In Toradora, Ryuuji slowly falls for Taiga.