This is a really hard question, because in the end it will depend on the kind of game you're trying to create. In most cases however, using a physics engine like Box2D might be overkill.
Especially for simple 2D platformers that don't include any physics puzzles, I'd go with doing the math on your own. It's not that hard to be honest.
To be able to stand on terrain and slopes, you just have to implement some very basic movement:
- Movement: When hitting left/right, just move your character to the left or right, don't worry about collision. Either move your character absolute distances or adjust his velocity.
- Gravity: Check to see whether there's something solid at the character's feet (depending on your implementation you might skip this check as you'll check it next anyway). If there isn't, move or accelerate him downwards.
- Collisions: After moving your character, verify he's not entering anything solid:
- Move the character to the right while his left part is in something solid.
- Move the character to the left while his right part is in something solid.
- Move the character upwards while his bottom part is in something solid.
- Move the character downwards while his top part is in something solid.
- If two opposite sides of the character are stuck in something solid (left and right or top and bottom), your character is squeezed. In games like Super Mario Bros this results in your character being killed.
Back to your initial question with the slope: Using the above logic, your character won't follow the slope at first. It will essentially move "into" the slope. But thanks to the logic under Collisions he'll be adjusted upwards, essentially following the slope up (or down).