Reinventing the pendulum (as in "reinventing the wheel)
So far, it seems, pendulum transportation had been used mainly for fun, such as in the case of swings. However, the principle could actually be used for transportation from house to house, either by building pendulums underground, or above the ground (in case of high buildings). You can even think of chain of pendulums one after another, extending over long distances. (Due to low friction, small extra energy is necessary to swing back to the original level on the opposite side.)
[Sorry, couldn't find a better category. The word 'Mass' in 'Mass Transit', is not in the sense of plurality, but in the sense of matter.]
Fun aspect: momentary loss of gravity every time you teleport.