During the Athens arc, Nagi telling Hayate that she didn't need money to protect her as long as she had him.
And don't forget in chapter 260 when Athena is saved.
The whole scene with Hayate taking Hinagiku onto the clock-tower balcony to see the view and her realizing she was in love with him (finally); using her fear of heights to highlight her deeper fear of abandonment and that even though she was still scared, it wasn't a bad feeling. Quite a few fans find it to be one of the sweetest moments in the manga, doubly so since Hinagiku is almost never that vulnerable.
The biggest is in 252, when Nagi sees that Hayate is troubled over the stone that represents her inheritance, takes it, and crushes it. When Hayate objects, explaining to her what it means, she just asks him to protect her now.
Also, before she crushes the stone, her statement that words can be misinterpreted (the entire premise of the story).
Chapter 300: Athena apparently not being able to resist hugging Hayate, even if it's only in a dream.
Chapter 81: Hinagiku befriending Ayumu and supporting the latter's intention to pursue Hayate...despite her own feelings for the hapless main character.
In chapter 307, Saki is looking for a new job and Wataru thinks she's leaving him because business is so bad, he can't even pay for her salary. In fact, Saki enver intended to leave Wataru and only wanted a part time job so as to help pay for his store. Wataru is so touched he immediately glomps her and cries.
The entire arc showing the backstory of Hayate as a child and his time with Athena was an Arc of Heartwarming for this troper.
Little Hayate and his grandmother walking through the amusement park.
Ruka admits that she has feelings for Hayate. A few chapters later, she actually KISSES him on the lips.
Hinagiku having fun with Hayate at an amusement park in the manga was very sweet but in the new anime, it's even sweeter. She even gets really close to Hayate and touches his hand and his reaction reveals that he knows what she is thinking. It is implied that they do hold hands.
Old man Sanzenin, despite being a big Jerkass, reveals his heart of gold underneath. Yes, he was the Santa who told Hayate to work for his dreams. Even when he had the chance to enter the Royal Garden, he didn't take advantage of Hayate and gave him hope for a better life.
Old Man Sanzenin: Didn't you hear? Santa is supposed to give little kids their dreams.