DVD

According to the Optical Storage Technology Association (OSTA), "manufacturers claim life spans ranging from 30 to 100 years for DVD, DVD-R and DVD+R discs and up to 30 years for DVD-RW, DVD+RW and DVD-RAM".✝

Blu-ray

The recordable media used in red laser disc technology like DVD's and CD's is an organic dye that is very sensitive to light. Blu-ray disks, however, use a combination of silicon and copper which is bonded during the burning process, this alloy is much more resilient than the organic dye. Manufacturers claim a life span from 100 up to 150 years for Blu-ray disks.✝

✝ = However, these media don't exist long enough yet to confirm or reject those claims. So at the moment, it's "about as long as the oldest working DVD/BD is still working". These claims are made assuming the disks are stored properly. (Not too hot, dark, not too humid, etc.) Furthermore, these life spans will be averages, I've used DVD disks that stopped working or showed data corruption after 2 years.