This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Kaleido Star
When Sora finds out that performing the 'Great Legendary Maneuver' with an almost broken shoulder injured Layla so badly that she won't be able to perform again in the Stage, she starts bawling. It's hard not to join in.
And what about Anna's Day in the Spotlight episode involving her fight with her father? When Jack performs the little trick with the hankie that he invented so many years ago to make little Anna laugh, I cried.
May Wong started as a pushy Spoiled Brat, but the episode featuring her fall from grace and subsequent Heroic BSOD is so well-done that you can't help feeling sorry for her. Then you actually grow to like her and are actually happy for her when she works to reclaim her glory.
Same goes to Leon, when he shows the first signs of his defrostment by panicking as he sees Sora almost being hit by a car just like it happened to his sister Sophie, pulling her away from danger in a Diving Save and, right after this, looking at her tenderly and asking "...Sophie, are you hurt? I'm so glad you're alive...", mistaking Sora for Sophie.
Yuri still feeling terrible guilt over what happend to Leon's sister tries to arange things so that Leon has the chance to take his life. And he goes to great lengths to make sure that if he succeeds he wont go to jail for it. The look of despair on his face when he believes he's about to get what he deserves is what solidifies his newfound status as The Woobie.