Killigangog: Good point, what's the deal with Mario being such a successful brand? One might think after 30 years of jumping around with the same onedimensional character, gaming society moves on?
I personally love platformers but I usually just don´t care about Mario titles. Yeah, I played Super Mario Bros 1, 2 & 3 back in the day, but they didn´t amaze me that much and I think I haven´t even completed any of them. There´s something about them I just don´t like. On the other side, I loved both Super Mario 64 and Super Mario Galaxy. Those two titles are all about 3D platforming exploration. You have a somehow big level with tons of things to do, and you must explore the entire level to get everything. I would say too that Super Mario 64 has more in common with Tomb Raider gameplay wise than Super Mario Bros: It´s all about controlling all your different jumps and other movements to reach a part of the level.
Personally, it´s not about the character, the story, or even the graphics. A good platformer needs good gameplay: You should be able to play right away without any kind of tutorial or manual, but you will need to know the main engine like your own hand if you want to master it. In that matter, they are like shmups: Everybody can move around a screen a shoot from the first play, but few will master the game totally.
And I´m not even talking about bosses. If there´s a genre where bosses shine is this one. There are even some platformers (like Dynamite Headdy), where there are more bosses than actual stages. A good boss fight is one of the most awesome experiences in videogames.
BTW, I´m not talking about generic platformers which are just Mario clones with a jump, maybe a run button, and meh level designs, I´m talking about the good ones. I know there´s plenty of bad platformers too out there, just like in any other genre.