So this sort of behaviour probably exists in other games, but the old Kirby games - Kirby's Adventure and Kirby's Dreamland 2 - is where I noticed it.
So, when dealing with regular block platforms, Kirby's hitbox acts like a simple rectangle, as you'd expect, as evidenced by the fact that you can stand like so:
On the other hand, when dealing with slopes of any kind, standing on them looks like this:
As you can see, if we were still using the rectangular hitbox, it would be halfway in the ground. This sort of behaviour is easily explained, however, buy a hitbox shaped like a 'diamond' or a 'plus'. (This is probably so that it doesn't look like Kirby is hovering in midair when walking on slopes)
Platforms such as these show perfect consistency with the 'diamond' hitbox model:
However, of course, the first screenshot shows that it's not possible for a diamond-shaped hitbox to be used all the time, or you would be able to 'slide' off any corner as if there was a slope there.
In fact, formations such as this show that it can't even be based on particular tiles, at least not 'full' tiles. (16x16, Kirby's size) (Otherwise you couldn't walk all the way up that slope)
Another model I've come up with is that the hitbox is always rectangular, but all slopes in the game are actually 'sunk' deeper than the tiles would have you believe. However, the stake-shaped platforms in the third & fourth screenshots invalidate this model, since then you wouldn't be able to stand at the top middle like you see there.
By the way, slopes on the ceiling work symmetrically, as can be seen in water stages.
While it seems intuitive to the player, how could we program a similar collision system ?
N.B. I am not asking for speculation on the internal workings of Kirby (unless someone here actually developed the collision system for those games - unlikely). Just a general approach.