Lots of the above, but if you're looking for non-classics:
Try a game called Kid no Hore Hore Daisakusen (otherwise known as Booby Kid on the NES, it seems). I found myself completely addicted to that game some months ago.
Also, a game called Trick Trap (a.k.a. Labyrinth Runner). It's another game I find myself strangely attracted to. Don't know why really, I think it reminds me some old Konami games I used to play on my MSX. Maybe it appeals to you too.
edit: Oh, I forgot: Rally Bike / Dash Yarou! One of my first non-classic discoveries on MAME. Still one of my favorites.
On the classics front, I think there was a vertical version/hack of Rally-X. I don't know what's the status of its emulation. It seems it was on MAME some versions ago, but was removed.