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In Music Of The Vampire, Shaggy thinks he's been bitten by a vampire (he was actually grazed by an errant stake) and seeks refuge in the swamp. He tells Scooby to let him go it alone for fear of turning into a vampire, and this potential split up is heart-tugging. Shaggy can't do it, as he and Scooby suddenly reunite.
In the Live Action movie, the entire gang splits after Velma quits, leaving only Shaggy and Scooby. Shaggy drives the Mystery Machine away while Scooby looks out the back window for the others, heartbroken.
Shaggy: Looks like it's just you and me now, Scoob.
A meta example is the treatment the franchise gives Scrappy Doo. He was created as a way to appeal to the younger audiences, but the result ended up backfiring and nearly everyone hates him. It doesn't help that Cartoon Network and Warner Bros. continues to take jabs and jabs at him, despite having a rather small, but strong fanbase. To put the hatred Scrappy gets is...an understatement.