I can think of a photo for which I would choose extra-large borders. Not the frames, but the area between the frame and the photo. 'Matting' the photo, as rfusca explained the term (new to me).
In the photo I have a girl sitting on a smallish rock by a lake, her feet in the water, and face slightly downcast as if she is in her thoughts, far away from present moment. That is her privacy, the lakeside rock, alone there for quite some time. What is she thinking? Perhaps her unborn fatherless baby and her future life with the baby? Can't really tell. But this photo I would put in extra-large borders.
How large? I think I'd make the photo 4" x 4" so that hanging on a wall it would be almost hard to see. But the frames would be at least 5" distance from the edges of the photo to the frame. Totalling in 14" x 14" area inside the frames. That way, I'm trying to distance the person, who is watching the photo, from the girl, who is having her private moment in time. And you don't dare to go closer.
The border around the photo acts almost as a tunneling effect, because you are not seeing anything else in the photo but the girl. The border is large, so it suggests there is a lot of more to see around, the nature, a field of hay or bushes, but you can't really see anything else but the girl sitting over there. The girl has enchanted you.
Back to the question here. I don't think the space around a photo is just wasted space. It is a style, or effect, or a message. I have photos framed to the edge with no borders at all, to bring the subject up close like you were right there yourself in the moment. (Not only at the moment, but in the moment.)