I've heard/ read that with spur drive sprockets for Stihl, 2 chains equals new sprocket. I think that this is going to be premature quite often, and also possibly overdue with others. Climbing saws don't usually need to be sharpened very often, at least if cutting a lot of softwoods. My 192T has the original, 3yo, spur drive sprocket. Some of the smaller saws use spur drives also as a one-piece deal with the clutch drum. They will go through chains with many fewer hours, as they are more likely limbing wood up on the ground, after its dropped onto dirt and rocks sometimes.
On larger saws, there is usually a rim sprocket which on Stihls, has holes on both the inside and outside. I've heard that the rim sprockets are worn to the point of replacing if they allow the drivers to touch the clutch drum (can be seen with chain off the saw with a chain put into the sprocket, and by the little dimples on the clutch drum. On Stihl sprockets, there is a little horizontal line that appears across the driver hollow, once worn enough.
This is a good question that, I think, needs a more qualitative answer (excess drag, bogs in cut easier), rather than quantitative (every 2 chains). Also, can people voice the repercussions of using a worn out sprocket?
