I've used them. I really like what they do. The main problem is simply the learning curve: getting people to remember that they have them and use them consistently (which is hard for a DM as well).
The upside is that it rewards martial characters for reaching high levels, and shifts the overall math towards defense without altering the economy (since usually, a D&D character's offense is skill and his defense is equipment). It gives characters tactical choices without adding any resource tracking (at least, beyond the number of actions in a round) and without doing anything that reeks of the supernatural.
my biggest concern is that the players will take to using either Dodge (bonus to DR) or Parry (bonus to AC) virtually *every* round (hey, if there's no AoO's in sight, why not?), thus making them harder to hit/damage, and slowing combat down.
Well, yes, but understand that you have to choose dodging or parrying for each attack you suffer. This provides a mechanical inventive for people to gang up on one enemy, as he'll run out of reactions pretty fast. It also creates a new dynamic for two weapon fighters; those first strikes are likely to be blocked, but you may wear your opponent out.
Battles probably do take a bit longer, but it isn't much in my experience, and well worth it for the tactical dynamics involved.
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One other thing I would note is that once you have a mechanic like this, it makes sense to create new class abilities and feats that leverage it more effectively. I included bonus combat reactions and bonuses for using combat reactions in several class rewrites that I did.