I didn't really have any "obscure" games when I was a child but I don't hear "Jackal" for NES mentioned in any conversation too often and that game was fuckin' RAD. It wasn't until middle school when I started playing computer games that I came across one that would take me another 10 years to finish: The Dark Eye.
The Dark Eye was a point-and-click adventure in the vein of Myst and was based on Edgar Allan Poe's stories and poems... And it creeped me the fuck out. Since when I first played it, it belonged to a friend. He took his game back and I barely found out the name of it a couple of months ago, found it on Amazon and bought it. <3
EDIT:
I had this really fun FPS on the Genesis when I was a freshman in high school called "Zero Tolerance" that got stolen a LONG time ago. Too bad too because I've never been able to find a copy of it anywhere since then.
Jam it back in, in the dark.