In general, what are the criteria to classify a barrel as worn out or need replacement?
Is that based on the number of shots or grouping results or something else?
Are there any recommendations for when to replace a barrel after certain number of shots?
A worn out barrel will not shoot well when it's burned up. You can't put a real number to barrels it all depends on how hot your loads are, what bullet types and if you let your barrel cool down between shots. All this factors in how fast you will burn your barrel out.
Excessive throat erosion, free bore and fire hardening cracks usually mean the barrel is done. If the fire hardening is substantial you wont be able to have the barrel "set back" and you'll need a new tube.
I think the indicator for most people is accuracy loss and random fliers. You can have a smith you trust bore scope it for you. That is usually the best way to know for certain. Many people think their barrel is toast when in reality its poor ammunition, a dirty action/bolt/barrel but more likely a poor shooter.
Over bore cartridges like many of the 6mm's/6.5mm's (6mmXC, .243 Win, 6.5x47mm, 6.5 Creedmoor, .260) will burn up a barrel substantially faster than say .308 Win or .30-06. Like Win_XP mentioned bullet weight, velocity and rate of fire (heat) have a lot to do with how fast the barrel will degrade.
Many people opt for chrome lined barrels to enhance life or some of the new fancy coatings/processes like Melonite.
Shows the "throat" A, free bore is where the lans eventually wear away and you have no rifling beyond the throat. (smooth)
Be sure to inspect the crown of the barrel, sometimes a nick or dent can cause a barrel not to shoot well but the barrel isn't shot out by any means.
Sorry, I should have said the numbers quoted were for 308 win caliber.
And, you are right, looks like for a 300 win mag, it's more like 1,000 rounds, according to Mr. McMillan himself. Was that typo, 1,000 rounds seems like a short life to me?