Most DVD Burners I've seen have a life cycle of 60,000 to 100,000 POH (Power on Hours).
Now that by itself is somewhat worthless because thats just the drive being on but not necessarly doing anything. But I have seen cited a couple places that the POH is cut to 20% with reads, and down to 2% with writes.
So...
12,000 to 20,000 Hours (1.36-2.28 Years) of reading.
1200-2000 Hours (50-83 days) of burning.
If you assume 7 minutes per burn (rough estimate for 16x on a 4.3GB disk) thats 10,285 to 17,143 disks.
Having said all that, I've had 3 die on me in the last 2 years.