Monitor glare can lead to headaches and can also adversely effect your posture since you may need to lean closer to the screen or off to the side in order to see well. Bad posture can lead to problems with RSI and other computer-related maladies (see, your mother was right).
Some obvious ways to fight glare are to get a flat screen or an LCD monitor–these types of screens are less susceptible. A cheaper fix is to get an anti-glare monitor filter. If you don’t want to spend any money, you can fashion a hood for your monitor using some carboard and tape–it may not be pretty but it’ll do the job.