Another meta example: This song by The Nobles, "Mandark". It's about how Mandark is Dexter's enemy because he pales in comparison to Dex and just wants to prove that he's also a genius. What's truly sad is that it's prettyaccurate to how Mandark was introduced and characterized (at least earlier on in the show), especially if you've seen "Mandarker" (mentioned below).
The wacky and fun episode of Dexter having to deal with Dee Dee's imaginary friend hanging out with him ends with Dexter wishing away the imaginary friend, and commanding him to never come back again. And he does. Dee Dee runs away sobbing. Then it fades to credits where Koosie just laughs and it suddenly becomes Nightmare Fuel.
Dexter feels so guilty that he finally gives Koosie the hug he's been wanting the whole episode.
The episode "Dee Dee's Tail" is about Dee Dee convincing Dexter to turn her into a horse and, as you can imagine, she is very happy... Until she realizes her brother and her friends just want to use her for rides, not caring if she is tired (even when she is lying down after taking her friends for a ride the whole day, all they do is show her a chariot they want her to pull). Realizing that the people you love just want to use you and don't care for your feelings is really sad.
Dee Dee: This is terrible... First my brother and now my best friends... [crying] I wish someone would help me...
As quoted from Fridge Horror: "When watching Dexter's Laboratory, if you think about it too much, you'll realize what a cruel, destructive scumbag Dee Dee really is. When she's not completely destroying her brother's life's work, she at times openly belittles, insults, humiliates, and abuses him for kicks and giggles." You need only look at such episodes as Road Rash, The Big Cheese, LABretto, Framed, Sister Mom, Dimwit Dexter... you get the picture.
This is doubly worse when you think back to the few times that Dee Dee herself is in trouble. You can tell that despite everything, Dexter has some serious Big Brother Instinct going on, despite being the younger brother who gets put through hell by his sister. That says nothing good about Dee Dee and a lot of good about Dexter.
Dexter's slinking away from his family in Old Man Dexter after being shot down when wanting to spend time with them because he's not old enough is treated to a few oddly long shots without any comic gags in them. Anyone who was the youngest child (or The Unfavorite) in their family can identify with him.
The Gratuitous French episode. He's solved all the world's problems with the term omelette du fromage. One problem— it's not the password of his Laboratory. He panics as the Laboratory erases its memory banks and shuts down.
...if by "shuts down" you mean "blows the fuck up" as Dee Dee taunts him...
Seeing young adult Dexter in 'Ego Trip'. It's really depressing to see Dexter, a boisterous, precocious little boy become neurotic and cowardly. The scene with Mandark whipping him is especially hard to watch.
In his first appearance, Mandark forcing Dexter to shut down his lab—
Computer: Dexter...what are you doing, Dexter?
Dexter: [tearfully] Goodbye, my love.
Computer: Goodby— [is cut off by the sounds of everything shutting down]