Gin no Saji certainly fits. The heroine Mikage spends much of the portion of the manga that was animated thinking of the hero Hachiken as a friend and completely oblivious to the possibility that he or ANYONE could possibly harbor romantic feelings for her. It all keeps going until...

Hachiken asks Mikage to go out just the two of them after a school festival. This in itself doesn't phase her a bit, until she talks to her friends about it and continues to insist they're "friends" until they all start ranting at her for being too dense to notice Hachiken's incredibly obvious advances. And even then they need to work to convince her that all the baggage she comes with shouldn't stop her from at least dating a bit.

If you're cool with light novels or anime, you could try Tamako Market; that girl is frighteningly dense.

3-gatsu no Lion certainly fits. It takes a while before the hero begins to fall in love with his heroine, but when he does she's very dense. He even declares to her deadbeat father that he's planning to marry her (to explain why he has reason to participate in a family discussion), shocking everyone, but a day or two later she talks about how cool he was making up such a "wild story" to drive the deadbeat away.

And lastly, a series I don't really want to recommend due to my feelings about how it's looking to end (I shipped a little too hard), but Momokuri has a character named Yuzuki who in my experience may be the reigning queen.

Yuzuki isn't the main character, but she and two childhood friends Shouta and Rihito became the center of a major sideplot. This girl is the object of some very strong love from both boys, and simultaneously pines after one and sticks like glue to the other, but remains completely unaware of anything outside of her crush on the one boy. She doesn't even notice how her affections for the other boy are so huge that absolutely everyone thinks they're practically soulmates. She thus spends more than a hundred chapters stringing two guys along, both seriously in love with her but unable to act because of her feelings for the other, blissfully unaware of the way she's been torturing them both for years.