I remember watching the first episode of Ed, Edd, 'n Eddy with my older cousin (grew up an only child, he was basically my older brother at the time). During the intro I said it was stupid, but he insisted I kept watching. It ended up being my favorite cartoon of all time.
I don't have any strong memories of Billy and Mandy. I do remember enjoying it, but kinda lost interest in the later episode because of Mandy going from kinda-twisted straight man to infallible and outright villainous who always won. I still quote one scene though, which was the episode with Billy's fish gaining intelligence, and Billy starts arguing with Mandy, tries to get his fish to support him, and the fish responds with, "I would prefer not to get in the middle," which is something I say (Austrian accent and all) whenever my friends try to involve me in a non-serious argument of theirs.
Kids Next Door I didn't like for most of its run, partly because I was in that "takes things way too seriously" phase, and criticized the show for having kids whose technology was better than the government. In retrospect, it was a pretty solid show, though.