Now before I create panic and mayhem, let me just state clearly that it is normal for some damage to occur to hair in the process of grooming it. The real concern comes if grooming causes more damage to the hair instead of helping it look neat.
Ok, having said that, let's look at what the research says
Damage from dry combing hair
1. The combing motion can cause hair to loop or knot (more force needed to comb, more chance of breakage)
2. Hair breakage - Long segments (where hair breaks off closer to the scalp) and short segments (breakage at the ends) of hair are often seen, with many more short segments.
3. Cuticle damage (chipping or breaking) due to increased rubbing (very aggressive combing can actually strip the cuticle completely off)
4. Last and probably most important - the more times you comb, the more the hair breaks.
Damage from wet combing damage
1. The presence of water allows the hair to clump which decreases short segment breaking but increases long segments. (Meaning the ends break less but breakage does still happen)
2. Increased hair swelling (caused by water uptake) can damage the cuticle (meaning damage to the cement that keeps the cuticle layers together, leading to cuticle weakness and chipping)
3. Unlike dry combing - increasing the number of comb strokes does NOT cause more breakage(probably because there is less friction between the wet hair and the comb)
I could go on but I think I'll stop here for today. Before I sign off, I would just mention that there are ways to reduce the amount of damage happening to the hair. You can read them here on Friday!
Int J Cosmet Sci, pg 76, 2008 (thanks to MH)
J Cosmet Sci, pg 477-84, 2007
Chemical and Physical Behaviour of Hair by Clarence Robbins
J Soc Cosmet Chem, pg 39-52, 1995