Two rounds minimum.  Maybe an extra 9 holes in the evening.  By then they go to a shag bag until I hit them out into the woods behind the house.

Until it goes into the water, the woods, or if it gets scuffed.  For me a ball lasts 6-9 holes.

I think it really is more of a preference thing. I know that I never want to look down on a really bad scuffed up golf ball. For me I will take a new ball out at the first of the round then grab a new one for the next round. 

I just finished my 4th round with a ProV1.  72 holes and counting.  No scuffs, they hold up to my iron and wedge grooves better than the TM and cally balls ever did (they would end up with groove-gouges out of them).  Best "bang-for-the-buck" ball I've found.  No point saving $10 a box if your ProV1 lasts ten times as long.

How long?  One round, but not because the ball is no good.

I alternate holes using two new balls a round.  If I don't lose them (possible) or make a birdie (rare, but possible); at the end of the round, I take the used balls out, mark the year, course and score.  Then I put the balls in my practice bag.

I imagine they would last three-plus rounds, if I kept using them.

I think the ball will last until the core is compromised. I try to use 1 ball per round and will reuse those balls on lower tier courses. I believe the ball plays the same from the first hole to the 36 holes if you dont hit a cart path, tree trunks, or put it in a lake.

Great point Chris!

I tend to change out my ball midway through the round depending on how the cover is holding up to wedge play. My full wedge shots tend to chew the ball up so if I have 1 or 2 of those on the front 9, I switch it out. With that being said, I wonder what the technical drawbacks would be if I kept it in play for the full 18. My bet is that it would be fine, the cover is far more durable than the balls of the past.

Lastly, I rarely start a round with an old ball. I like to start on #1 with a fresh outlook and looking at a ball from my last round doesn't always help. 

I end up going through 1 or 2 a round because I scuff them with my wedges, and occasionally scuff them on an errant shot....if I had an endless supply of balls id probably go through a sleeve or more per round.   It does depend on the course, I find shorter courses where I hit more wedges I end up with more groove marks on the ball.  Although I didn't have that problem until I put the SM5's in to play.