This may be couple of stupid questions but here I go:

On a semi-auto like an AR, does excessive headspace in the chamber usually render the barrel assembly "worn out" first or does the barrel rifling usually go first?  

After how many rounds can one expect one or the other to happen and can a gunsmith fix this or is it time for a new barrel?

Excessive headspace - if it can't be fixed by using a new bolt - will require a new barrel.

Usually you wear out the throat or rifling before you strecth the chamber enough.

As for how many rounds it can take that depends on the barrel material and how it is shot (lots of full-auto fire reduces barrel life).  You can read hear about barrel life: groups.msn.com/TheMarylandAR15ShootersSite/barrelfaq.msnw (near the bottom)

"Barrel stretch" causing excess head space??? After fifty years of firearm ownership, and 30 years of maintainance and repair for myself and others, I guess I'm learning something new

Look, in today's firearms world, the probability of a previously OK rifle developing excess headspace is so small as to be practically nil. It was far more an issue in the early days of smokeless powder ammo, when heat treatment of firearms steel hadn't caught up with advances in ballistic performance and pressure attainable with the new propellent. Head space is, or can be, an issue, when swapping bolts around, or replacing old bolts with new ones. If the headspace on your AR is OK now, it's 99.9% certain to be OK 10,000 rounds from now.

Throat erosion is another story. Yes, it occurs with all high power, jacketed bullet firing rifles, and several factors can accelerate the process, or retard it.  Extended and extensive rapid fire (and full auto of course) will accelerate it.  So does the use of boat tail bullets, which most all 5.56 ammo has. Using flat base bulleted ammo will retard the erosion, and many barrels eroded from extensive use to the point where military boat tail bulleted ammo will start key holing their shots, can be brought back to a decent accuracy level by switching over to flat base ammo.

Chrome lined barrels resist erosion better than unlined barrels, but once they start eroding significantly, they tend to lose accuracy  faster than unlined units.  My own position is, hold down the bump (or full auto) firing, use ball powders if you handload, and stop worrying about it.  Oh yeh, don't get "clean crazy" scrubbing out the barrel. You're likely to put more wear on a barrel witha cleaning rod, than with bullets.  Keep the action clean for function reliability, but one simple pass with a dry patch is usually more than enough after a day at the range.  

If you were installing a G.I. barrel on an Upper and your torque it to specs., does this automatically set the headspace?  Or, is that a separate measurement?  Pardon my ignorance; I'm still learning how to build these things!

No. Headspace is set when the bbl extension is fit/installed by bbl manufacturer.