IMO, Platformers all games where you control someone who walks and jumps, in a sideway point of view.
I think platformers games can be divided in 5 main groups:
the Jump 'n' Run, like Mario, Sonic, Giana Sisters, Zool or Soccer Kid
The Shmups one: Turrican, Ruff 'n' Tumle, Contra, Alien Soldier or Gunstar Heroes
The Arcade Adventure ones: Flashback, Another World, Super Metroid or Gods
The Puzzle ones: Benefactor, Fury of the Furries, Lost Vikings
The "Kill everyone in the Screen": Bubble Bobble, Parasol Stars, Rodland, Snow Bros, The Fairyland Story.
And many times, a game can fit in 2 or more categories.
Out to Lunch, for example, fits in the 1st and the last category, an MSX game called "The Castle" fits in the 1st, the 3rd and the 4th category.
here I am, talking about the MSX again.
I've made a good list of platform games in a few posts above... just remember me, and I'll send you a few good ones. I am pretty sure I sent you Treasure of Usas, but I bet you want MSX 1 games now...
I also sent you The Castle and Castle Excellent. I know those games don't look impressive, but play them for a little while, they are two of the most fantastic, superb, marvellous games ever done in any system.. they are THAT good really, believe me.