It depends on both the material and how well you treat the tank.
For aluminum, many shops refuse to fill them after 15 years. This doesn't mean that they don't last longer than that--it's just that they don't trust them perhaps as much as steel.
With steel tanks, if you treat them very nicely, they could last you a lifetime. I saw an oxygen cylinder that was first hydro'd in the 1950s while working at a dive shop.
Generally, if you overfill a tank then most people say it shortens the life. Just to be on the safe side I would probably agree.
As to age before not passing hydro--I've heard of tanks that won't pass their first hydro after being purchased (assuming a new tank, 5 years from the purchase date) but these are quite rare. I've seen plenty of aluminum tanks that have hydro dates stamped down the side. If you can find them you can find some steel tanks with 5 or 6 hydro dates stamped in the side!