Super Mario Kart: everything was "nerf'ed" in the sequals. Anybody could easily learn to execute a multi-hit combo in battle mode because you could pick up a single item consistenting of multiple shells. In the original, you had to time your shots so that you could pick up another weapon to combo with. Red shells were also changed, so that dodging was less of an art form. In the original, they had strange and erratic behaviour that allowed for "Kung-Fu" like acrobatic escape moments, where you could outrun a red shell closing in on you and then twist and turn and hop around until the red shell "freaked out" and smashed into a wall. In the sequals, red shells basically just travel in a straight line towards their opponent, so dodging them is less fun. I could go on and on, but I must say that while graphics and sound have improved in the Mario Kart series... the gameplay has not.
Quake: Quakeworld is still the best Quake, at least in deathmatch. It is fast, furious, and has great small levels. The weapons are powerful, and the movement physics allow for lovely unrealistic Matrix-like acrobatic moves. THank god Id Software released the source code for Quake so that it could have its graphics slightly improved by the community, as well as the sound and other aspects such as adding a built-in server browser:
http://ezquake.sourceforge.net/gallery/