I'm in a constant battle with my shoulder and lat muscles over the "computer hunch," the tendency for my shoulder blades to round forward.
If you're not sure whether you have good posture or not, sit and ask a friend to lay a wooden ruler against your upper back. It should lay fairly flat against both blades; any space means the shoulders may be rounding too far forward.
Strengthening your core is a necessary and sure way to better your posture, but specifically targeted exercises are important, too.
Poor posture not only makes you look slumpy and older, but it can put strain on your back and cause problems down the road. Eventually your spine may loose its natural curves and it will be hard to get those once graceful and youthful lines back.
The trainer at the gym told me that the lateral pull down machine is one of the best posture-improving moves because it strengthens the muscles in the back that hold the shoulder blades in proper position.
Oprah.com also has a six-slide Posture Exercise Plan featuring stretches, positions, and moves.
Do you think you have good posture -- have you ever checked? How much do you pay attention to it when sitting at the computer or working out?