This plant was given to my grandmother a very long time ago by a kid she babysat. She gave it to me to take to college. I have no idea what it is except that it looks kind of like a succulent. I want to know what it is incase something goes wrong. I've been watering it whenever the soil looks dry (about once a week) and I keep it in my window so it gets light and it seems to be doing just fine.
It is Plectranthus verticillatus. The red-ish hue of the underside of the leaves will become more proeminent on the upperside too if you move this plant in full sun and water it more sparsely. It is drought tolerant after it has established itself. The flowers are white with very small purple-mauve dots. This plant doesn't need pampering. I have five pots and I neglect them, but they stay alive.
It is easily propagated by cuttings, just take a 10 cm (4 inches) part, remove a few of the leaves from the base and stick it into soil. Keep the soil moist until it grows new roots, and then you can water it only when the soil is dry and the leaves start to fade or to lose their shine.
Also, the person who gave me the original plant kept her Plectranthus in garden soil for many years and the plant was growing well. I keep my plants in potting soil because it's easier for me to buy it, even if this plant doesn't require it.
Update: In case you're wondering why the leaves are too thick to be Plectranthus, look at the leaves on the left side of the image and you'll see they are not thick, they curled on the edges:
Similar to this Plectranthus:
Looks like Kalanchoe..a succulent. I would put this in a clay pot with potting soil. The same size pot you are using now. More light. Watering seems to be good. Any fertilizer? Potting soil only!