"Skipper Dan", amid the theater and Disney references, is a surprisingly sad tale of a man whose dreams of success and fame were shattered by reality, leaving him in an endless rut working day to day to pay the bills and deal with his depression. Not nearly as tragic as other examples on this list, but far more likely to hit close to home.
"You Don't Love Me Anymore" might be far worse. Not only is the music genuinely sad, but it's about his girlfriend's attempts to murder him. The lyrics are intended to be humorous, but occasional lyrics like "you're still the light of life" and "my scars are all healing but my heart never will" implying the singer still loves the subject of the song might still bring tears to one's eyes.
"One More Minute" is a song about a man describing all kinds of painful things he'd rather do than spend one more minute with his ex, who is now seeing someone else; it's obvious, though, that all the painful things he's describing are how he feels seeing her with someone else and the only thing in the world he wants is to have just one more minute with her.
The Darker and Edgier version of "The Night Santa Went Crazy" ends with Santa's brains blown out on the pavement - considerably darker than Al's usual fare, and especially hard-hitting for anyone who heard the version where Santa goes to prison.
YMMV of course, but the Reality Subtext of the general disappointment of The Phantom Menace and the specific way it ruined Jake Lloyd's acting career, coupled with the elegiac tone of the song it parodies has given "The Saga Begins" a mournful quality. Just try listening to the last chorus while reading about how Lloyd eventually destroyed all his Star Wars memorabilia...