Here are awesome examples of where the sequels are better than the originals.
-Thunder Force 2 (they just kept getting better and better)
-Revenge of Shinobi (most people prefer it over the original Shinobi)
-Shinobi III (ditto)
-Super Fantasy Zone
-Castlevania 3 (I pretend that part 2 does not exist)
-Super Hang-On
-Virtua Fighter 2
-Super Mario Bros 2 (US version, I do not enjoy the original SMB)
-Star Trek II: The Wrath of Khan
Have you tried Thunder Force One? I've always wondered if its any good.
Although I can see how most people would consider the sequels to Shinobi to be better than the original, I don't consider them real sequels(
to Shinobi One, not each other), since they're so different from original the Rolling Thunder'esque gameplay.
I think you mentioned in another thread that you prefer the first SMS Fantasy Zone to the sequel. But FZ2 is my favorite, although I haven't really tried Super' and haven't played enough of the Game Gear game.
I think Keranu was talking about direct sequels though... which still doesn't change the fact that sometimes developers don't get a game right until they've ripped off millions of 'fans' with a few experiments (
I'm still waiting for the first good game from many hit series).
Virtua Fighter 2 is a great example. Its still my favorite VF game.
Wrath of Khan is an easy one, since the original wasn't very good in the first place and there's no 'magic' to try to beat.
GTA III, Duke Nukem 3-D, Super Smash Bros. Melee...
Although Duke Nukem 3D is a better game than the side scrollers, its like comparing Mario Kart to SMB.