The short answer here is, "Probably more often than you think." A bike chains job is to transfer every watt of power from your cranks to your back wheel, and that's a big undertaking. With performance bikes becoming lighter, and cassettes offering more gears in the same amount of spacing (i.e thinner chains), it's not uncommon for heavier riders to wear through a chain in as little as 1,000 miles. That's just a few months for someone who rides every weekend.
Rider weight, terrain, even wheel size and chainstay length can all affect the life expectancy of your chain so it's hard for us to set an exact mileage number for replacement.
Although there is no cut and dry length of time a road bike chain will last, there are several tools to measure chain wear, and some easy ways to extend your chains life. The best way is to maintain a clean and lubricated drivetrain. This means cleaning the grime off of your chain, and lubricating it every three or four rides. We love Rock & Roll Road chainlube, and a small bottle will easily last six months.