This is something that's been bothering me for the longest time and i have never found an at all satisfactory answer anywhere else.
What on earth do Sonic fans mean when they say "momentum based platforming" and often imply it's something at say Mario doesn't have? I would think any platformer in which your speed effects your jump and require you to build up to a run for some jumps or to race up hills would be momentum based platforming but it's often brought up as strange new thing Sonic invited.
Well, yes, pretty much every platformer out there that differentiates between "walking" and "running" has some sort of momentum-based platforming, generally in the form of jumps that can only be made if you do them at full-speed.
The thing that's a little different with
Sonic is the terrain directly influences how you jump - so, jumping at full speed when running up a 45° incline would potentially have you shooting off almost perpendicular to it, or doing so when running down would have a bit less effect. Not to mention, the steepness of slopes also factors a lot into getting up to top-speed quickly. I suppose this applies to
Mario too (with
SMB3-onward's hill-sliding mechanics), although it doesn't come into play nearly as often as it does in
Sonic since
Sonic stages roll around like skate parks more often than
Mario stages tend to. And then there's how, if you have enough speed/velocity/momentum/whatever and the angle between the floor and a wall coming out of it is gentle enough, you can start running over all kinds of surfaces willy-nilly, as long as you kept up your momentum (since gravity would be working against you if you were running
up a wall). I don't doubt other games had similar features (
Super Mario World's triangle block or the Baby Mario segments from
Yoshi's Island comes to mind), but they're usually limited to specific moments and aren't the basis of the entire game.
There's also how it ties into what passes for combat in this game. There's still the tried-and-true jumping on things when you're moving at a slower pace, but then there's the Spin Attack, which trades almost all control over yourself in exchange for even more momentum gain/loss and near-invincibility. It's a pretty inventive thing, really, letting you toy with the aforementioned slope physics even more (since your speed cap is significantly higher when you're rolling) with a bit more impunity (since you do damage to enemies while rolling, and thus will defeat them without taking any damage yourself), although not
total impunity (since you can't control yourself as easily while rolling, so if you haven't learned the stage yet you'll potentially roll into spikes or something - this isn't as common as the series' detractors imply it is, but I'm sure it does occasionally happen).
The end result is something just a little different from the average platformer physics, and it's a niche that not very many games have really tackled. Closest I can think of are those
Marble Blast games and similar.
Freedom Planet, too, for fairly obvious reasons (directly using a
Sonic fangame engine).