Tamaki's back story about him being forbidden to see his mother due to his grandmother's meddling. Made that much more of a Tear Jerker by the fact that Tamaki not only doesn't resent his grandmother for her horrible treatment of him and his mother, he is honestly happy to see her and calls her a "beautiful person". Aw, punkin.
Not to mention the way Haruhi first hears about it in the manga. The Host Club's at a school gathering where all the student's parents appear, including the Host Club's, similar to that in the anime.
As well as Haruhi's mother turning out to be the "queen" in the Haruhi in Wonderland episode. Considering how it was handled in the comic, this episode was quite an unexpected tear jerker.
Recent chapters of the manga have pushed Tamaki's woobieness past the breaking point (though he'd deny it for his friends' sake), not to mention his superiors doing something that was in the finale of the anime: Putting a stop to the Host Club.
Did no one else well up at the final anime episode? "We all love the Host Club! Even I love the Host Club!"
Well up? Try full-on sobbing by the time that line lands.
Kaoru's metaphor about Tamaki keeping the Host Club as a family is fairly heart-wrenching.
Most of the times Kaoru brings up his Carriage/Pumpkin metaphor are pretty misty. Capped off in the final episode of the anime when after racing the carriage Tamaki had rented for the festival to catch him on his way to the airport, the twins and Haruhi hit an obstacle and Hikaru ends up crashing into a pumpkin patch.
Kyouya getting slapped by his father. He tries so hard, and the one thing that gives him pleasure is thrown in his face as a failure.
That one manga chapter page with all the chibi hosts building a house out of blocks was the sweetest thing ever. Combination heartwarming and tearjerking.
"Hey Hikaru, she says she'll take you instead!" The pain in their voices... It hits a bit harder the second time around.
The twins deciding once and for all that they'll try to be their own person, but that they'll always be there for each other. It even breaks Kaoru into tears in a good way, after realizing that Hikaru was more mature than he'd ever thought.
The ending of Chapter 75, where Tamaki had yelled at Haruhi for the first time in a rather pissed manner, leaving her stunned. When she arrives at her house, it begins to thunder, and she quickly runs to find the ear plugs Tamaki gave her at the beach. While covering herself with a blanket, she thinks back to how he had comforted her during a storm before, and the chapter ends with her hiding under the blanket and crying.
The end of Chapter 82. "Yes, I will go...I'm going to America."