I got a piece of this plant from my Grandma who got it from her Aunt who had it since around 1920... and we can't figure out what kind it is. Any help would be greatly appreciated!
Yes, it's one of the many haworthias, although the leaves look a little elongated. Make sure it's getting good light with a few hours of direct sun.
I will second H attenuata. Get the plant into full sun, and it will be a smaller, white striped plant.