That's something I notice when I take mushrooms. Instead of seeing "my hand" I see veins, skin, bumps, tendons, shadows and a lot of other things. I think a lot of great artists either see like this always or maybe they are taking psychedelics to help.
Not even need for drugs. Just give a good, intense, long stare at your hand. I bet before long, a weird sense of "this is not mine/me" or it being very uniquely unique, rather than a "hand", or being an empty set of parts, etc. will emerge.
Or, alternatively, you can consciously switch how you see it. A hand. Me. A bunch of molecules. Remnants of an old supernova. The results of millions of years of evolution. The tool with which you can communicate the depth of your love to your child by gently stroking them. Just actively changing the "name" you give it will change the way you perceive it, sometimes subtly, sometimes quite radically.
If you are interested in this kind of things, I would recommend the teachings or Rob Burbea. His whole works are built around exploring this topic.
I think for me psychedelics are a good tool to learn observations like this. Now I often can recall this state without taking any substances. I think my meditation also has improved.
A pleasant surprise to see Rob Burbea mentioned. I recently started listening to his Gaia House retreat from August 2008. I've heard nothing but good things said about him.