Keep your chain (relatively) clean, lubricated and gauged. At every cleaning, inspect it for cracked links, excessive plate spread, tight links, etc.
Replace your chain at the recommended wear point. As dhk2 pointed out, 1% is specified and recommended by several sources. Personally, I toss my 11-speed Campy chains at 0.75%. That's right around 1,500-2,500 miles and I usually get 3 chains per cassette replacement. As a rule, it's my most used flat road ratio and my two steep hill climbing cassette gear teeth that show the most wear...no surprise there. High pressure use and high percentage of use gears.
The last 53 tooth Record chain ring I wore to the point of replacing went somewhere between 25,000-30,000 miles, thanks to keeping clean, lubricated and in-spec chains on the bike.
Another advantage of keeping your drive line well maintained is solid, fast and accurate shifting in addition to Watt-saving, smooth running, quiet power transmission from the pedals to the wheel.
Most importantly, a broken chain can lead to instantaneous loss of control of the bike. On a deserted road that might mean 'only' a hard crash and some cuts and bruises. If it happens with traffic around it can mean death or serious injuries from flying into traffic.
When 9 and 10-speed drives first hit the market there seemed to be an epidemic of broken and snapped chains and recalls of those 'quick links' or 'power links' used as master links. Improperly sized chain tools and low quality chain tools contributed to the problem as did little or no training / education of those using the tools on the new gearing systems.
Between faulty manufacturing and user error everyone from bike store employees to Pro-Tour mechanics to home maintenance users were screwing up chain replacements and installs and result was broken chains all over the place. It seemed every televised pro race showed a picture of some ****** off racer standing by the road side with a broken chain dangling from his bike.
For probably a number of reasons...more experience with the critical nature of the products and improved designs in product and tooling foremost...the number of chains that 'explode' apart appears to have been significantly reduced. Maybe it's just my observation, but I just don't see or hear about the issue nearly as much as I did say...10 years ago.
A bicycle's driveline integrity is absolutely critical to maintaining control over the machine when you need that control the most...when pedaling under high pedal pressure such as climbing, accelerating the bike or powering along at high speeds. These are especially poor times to find yourself suddenly NOT in control of your direction of travel due to the dreaded 'air pedal'.