This is based on opinion. Please don't list it on a work's trope example list.
Tearjerker / White Collar
Neal's drugged confession to Peter in Vital Signs.
Neal: Out of all the people in my life — Mozzie, even Kate — you're the only one.
Peter: "The only one" what?
Neal: The only person in my life I trust.
The moment right after where Peter steals the tape of Neal that would have landed him back in prison makes me tear up, too.
In Unfinished Business, Neal and Mozzie visit the hangar where the remnants of Kate's plane are kept. From the moment they step inside, Neal can barely keep it together.
Neal rescuing Peter in Company Man, particularly this exchange:
Neal: No! No, Peter, we don't have time!
Peter: You can't leave him behind.
Neal: You are dying, Peter!
Peter: Neal! ... Neal, we don't leave anybody behind.
[Neal gives Peter a desperate look and then runs off to save Kent.]
Judgment Day: There was nary a dry eye to be found.... well, there was, but to quite a bit of the White Collar fandom, the end of this episode made them tear up.
The end of Parting Shots. Jeff Eastin's tendency to use titles with double meanings has never been more cruel.
Mozzie's shadow-puppet show in Identity Crisis, in which he tells the story he made up when he was a kid to try to rationalize why his parents abandoned him.
Neal: It's a really great story.
Mozzie: That's all it is, Neal. Just a story an eight-year-old tells himself to hide the fact his parents didn't want him.
This scene is the only time we ever see Mozzie cry.
But it also doubles as a Crowning Moment of Heartwarming, as it shows how good a friend Neal is to him. He insists that Mozzie show him the shadow puppet show, sits attentively through the whole thing, and then comforts him when Mozzie breaks down.
This episode we learn that Mozzie kept all of his schemes connected to his real name. Why? So his parents would be able to find him if they ever came looking.
When Neal says goodbye to his father at the end of Family Business.
The flashback to a three-year-old Neal happily telling his dad goodbye as James is leaving for work makes it even more heartwrenching.
The end of In The Wind. Seeing Neal in tears as he begs his father to stay and testify after Peter is falsely accused of killing Senator Pratt is absolutely heartbreaking. The utter desperation in his voice as he pleads with James.....
Neal: You show me you're better than this! You show me you're a decent man!
My gosh, Matt Bomer deserves an Emmy for that performance!
The death of David Siegel, Neal's new handler.
Peter saying that the reason Neal took the gold was that he was a criminal and that's what he did, when Neal was trying to explain that he only did it to help Peter. The look on Neal's face was both shocked and heartbroken.
Peter telling Jones not to volunteer to be Neal's next handler, telling him he'll regret it all while Neal is listening in via bug.
The second half of the series finale is basically nothing but tearjerkers, with Mozzie and Peter sharing their grief.