Depending on the upkeep, I would guess a .22LR would go in the neighborhood north of 10-15k rounds and still give "minute of squirrel" accuracy.
Of course, on centerfire rifles, there are a lot of variables to keep in mind, with the most important being heat. This is even more true for high velocity centerfire cartridges, specifically those with muzzle velocities over 2800-3000fps. Let the barrels heat up too much on these rifles, especially a small caliber such as a .22-250 and .243, and you can ruin a throat in less than 1k rounds (if not 5-750 rounds). Keep the barrel cool, and you can expect a barrel to give sufficient accuracy out to 4k+ rounds.
Now, "acceptable accuracy" is subjective. A deer hunter, quite frankly, is likely to never shoot out a barrel. In fact, its more likely the barrel would rust out before it was shot too much. A bench shooter, on the other hand, may consider a barrel ruined after groups begin opening up .2-.3". Actually, I have talked to a few shooters who were rebarreling after groups "opened up" to .5" at 100 yards.
Reality is, very few of us will ever shoot enough to truly ruin a barrel. I have heard it told from several 'smiths that more barrels were ruined from improper cleaning than any other method, shooting included.
