Begonia hatacoa 'Spotted'? Wikipedia does not list Begonia maculata as a synonym, but a query on the hatacoa name brings up maculata as well, maybe because both are known as angel wing begonias.
A horticultural category for various begonias of this type is cane-stemmed begonia. These usually grow upright - notice that the second cane growing up out of the pot on the right is pointed toward the ceiling. This is how the whole plant wants to grow, with the larger cane tumbling down from a point where it appears to have become bent or broken because of environmental conditions where the specimen is currently situated. Low light levels for instance.
I got this plant from a friend who had it on top of her fridge, so I guess it had to grow down to get to the light. Do you think I should trim the plant back, and put it on a windowsill, so that it can regrow upright?