It's gonna sound weird if 'you werent there at the time', but when the original Super Mario Brothers came out, the controls were incredible for its time. You had unprecented controls over Mario, it was very fluid, it just felt perfect, the scrolling, the jumping mechanics, for the time, it was a huge advancement over other tiles (on home consoles and arcades). The 'physics' were unmatched.
Mario 3 introduced the flying elements and once again, it felt so great compared to other titles of the era. It was really fun to explore around. Super Mario World perfected the flight mecanism with the cape and introduced tons of new features like the spinning jump, riding yoshi, the different variants of Yoshis, etc etc. It felt like an evolution.
Then Mario64 came out and Nintendo outdid themselves with the 3D controls, the different stunts and jumps, etc etc.
Ever since.. Well it feels like half-assed ideas, remixes and rehashes of previous concepts. Mario Galaxy was a nice concept, and a nice game overall.. But to me it really like like a bizzare gimmick to base your entire game on. It feels like it would had been a nice interesting idea for world in a regular mario game (kinda like the giant world in SMB3) but having an entire game based on this felt like they ran out of ideas. I didnt get very far simply, I simply gave up on the title.
As for the New Super Mario line.. Well it just feels uninspired. The levels feel 'strange', they all have that 'romhack' feel to them. You can tell that a new generation of developpers is behind this one, and it shows. The games are not bad, they are well made, well put together, but it really feels like it's stalling. Nintendo used to be at the top when it came to coming up with new designs and ideas, and their platformers really destroyed other products of their eras, they just felt that much advanced.
But now? The titles are very 'safe', they all have that 'design by comitee' vibe, they are following a recipe without having any kind of inspiration; the magic is gone. Maybe it's just that the decision makers at Nintendo are now old and they want to take risks, but eh.. That's why I feel like Nintendo's platforming design peaked with Mario 64.
Mario was ALWAYS about acrobatics and having excellent controls that allowed you to do nice 'runs' like in that gif posted earlier.