A lot. See some of Progress's comments about the spinal column in his thread, Progress on Progress. Basically, there's a connected system running from your tailbone through your skull, and it has an ideal balance and alignment for health--see Esther Gohkale's book, 8 Steps to a Pain Free Back. The rounded shoulders are indicative of other misalignments that affect your face, your skin tone, your teeth, your sleep--all sorts of things. In addition to the things I mentioned above, also have a look at Ronald Ead's blog and videos on posture--they are very relevant to your question.

I have similiar problem, have hunch back posture for over 10-15 years from sitting at computer desk for very long hours. I think it may aswell have caused problem with my hips, they are so blocked, I run into a problem called FAI, and now im trying to stretch the muscles to free my hips.
BUT going back to the topic I recently ran to a nice tip on reddit for getting your posture straight and your tongue automatically sits on top of the palate, its hard to cheat in this position: get your hands behind you, link them and pull them down so your shoulders will retract; you can add a bit of a chin tuck aswell to strengthen the mewing effect.

@adam

Try some third world squats and youll be back to normal very quickly. At first if you have to holdonto something in front of you thats fine but do that stretch everyday and your hips will open up