For some reason, in "Fanning the Flames", Ember's song is curiously wrenching. Mostly because the fandom consensus (despite the bad fic written about it) is that it's about the suicide of the ghost singing it, after either losing her virginity or finally committing herself to her boyfriend in a serious way only to be discarded.
For dog lovers, there are tears over the death of "Cujo" the ghost dog where the series hint that it may have been put to sleep. A ghost PUPPY.
There's also Vlad himself. Since he's a villain with sympathetic goals, it isn't hard to get really, really emotional during his Villainous Breakdown in the Season Two Finale. For months, he's ached for Danny to be his son and while he tried to get it in the most diabolical manner possible, the fact that he had to see his perfect clone—nay—his perfect SON dissolve slowly right in front of his face while reaching out towards him was just heartbreaking. His huge Big "NO!" just sealed the deal. The insult to injury? His son was killed by Danny himself. Goddamn it...
And also, his final scene in the last episode where Jack leaves him to rot in space after realizing his best friend had "died away" twenty years ago. That's not the sad part; the sad part is when Vlad realized how much of an asshole he's been. He gives off quite possibly the most saddest face ever and flies away into emptiness that he's feared all his life. No words, no goofy comedy—just sad music as his expressions tell it all. * sniff*
The Ultimate Enemy. Both of Danny's friends, his parents, and his sister die in a tragic accident, which if blame is to be assigned, it would go to Danny for cheating on a test. Then, he's sent to live with his arch-enemy, where he tries to get rid of all the grief he's feeling. This leads to essentially killing himself along with practically everyone he could get to. Eventually, this evil Danny goes back in time to kill everyone he once loved only to ensure he'll still be just as evil in the future. And, the statues: Sam, Tucker, Jazz, Maddie and Jack: "Gone but not forgotten." Mr. Lancer: "Gone"
It's when Danny visits this future's version of Vlad Masters . It's the most sympathetic we see the guy in the series (except perhaps for the end of Phantom Planet.) Vlad has spent ten years with nothing but his own guilt to keep him company. Ten years of having to face the fact that his best friend, the woman he loved, and the boy who he wished more than anything would call him "dad" are all dead, and that it's all his fault.
Likewise, freakin' Dark Danny's (Dan Phantom's) fate in TUE can be considered something of a Tear Jerker. He's doomed to be trapped in the Fenton Thermos (even though he's shown trying to escape..he's never seen again in the series), alone, with nothing but his insanity and his rather tragic memories to keep him company. Though seeing he's The Sociopath with no human emotions, and last seen with a Slasher Smile, it may be somewhat difficult to sympathize with him.
Dani. Created by the villain in order to try to defeat the hero, combined with the fact she probably feels at least somewhat similar to Dawn in Buffy, as well as her being voiced by Anna Sophia Robb, who's played Break the Cutie before, and you've got a Tearjerker.
In "Masters of All Time", Jack suffers the same accident that caused Vlad's canon state. However, he is even more sympathetic, because he isn't amoral enough to use his ghost powers to become rich or manipulate his enemies. And then we have this:
When Valerie breaks up with Danny at the end of Flirting With Disaster because she doesn't want him to get hurt because of her ghost hunting (not knowing that he is Danny Phantom, the ghost she hates so much). Danny's really good at looking like a kicked puppy.
The Christmas special has one of these when Danny destroys everyone's toys used to form the giant nutcracker.