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One of the more interesting concepts to me it 2D rectagles [sprite objects] on slopes.
Try putting a square on a triangle. Most games put it in the middle of the character, some on the inner pixel of the character leaving the entire character except one pixel off the slope, and some put it into the hit detection on the outside pixel letting the player walk into the block before the slop starts getting moved up on. There's many different types, but those seem the most used, those 3.
One example is Kirby for the NES which has 3 slope types and does it by changing the standing animation for those to conform to the slopes. It hit detects in the middle so even if it conforms to the slop, it will still float or be into the ground when the character is on the edges of a slope that goes into another surface.
Sonic for Genesis puts the slope hit in the middle of sonic on his feet, and then on flat surfaces move the block standing detection to the outside dots. That's why you can move off a sloped hill and then fall down 1 block and land inside the hill.
MC Kids for NES puts the hit point in the middle for the hill and that's it. Simple and straightforward, although half the character is always floating in the air.
No solution is perfect, some take more characters, some don't do anything, and it's a very interesting topic to me. You can of course just use characters for all combinations of slopes, but for games on older platforms that's not plausible, and today is still a wasteful way of doing it.