As a desk-bound office worker, I know first hand the perils of sitting down at a computer all day. (And then coming home and sitting down some more, at a different computer!)
Many people don’t realise that their stiff shoulders, stiff necks, upper back aches and pains etc, are possibly caused by poor posture at computer desks, and poor sitting postures in general. One of the worst things is the ‘forward head’ position.
There is an excellent article on Yoga International which outlines the problems of poor posture, the symptoms, and what you can do about it to try and relieve the muscular aches and pains.
One of the three suggested stretches are covered in my recent 5 minute neck video (ear to shoulder) and one in my shoulder video (elbow circles or angel wing circles as they call them). There are also two floor based exercises they recommend to counter the over-tight front chest.
I would also recommend going to a good massage therapist as a preventative approach to ease stiff and tight neck and shoulders.