I spend a lot of time in front of the computer too. Here are a few things that can help to mitigate the negative effects.
Get a stand up desk so you're not spending all that time sitting.
Move around to avoid being in the same posture for more than 20 minutes or so.
As much as possible, be mindful of not slouching.
Have your monitor in a position where you can look at it with your head in neutral alignment.
As basic part of good posture, try to keep your chest up and shoulders back without giving up neutral alignment of your ribs and pelvis.
Keep your chin tucked in to maintain a neutral rather than forward head posture.
Some good exercises to maintain range of motion in your neck are: rotating your head up and down through the full range of motion, then side to side (as if looking to the side), then side to side (ear to shoulder), then chin to collar bone. Other than that, the best exercise is simply taking a break from the computer and moving around or doing regular mobility exercises.