It depends. Traffic/user sessions and existing conversion rates play a big role in how long a test needs to run to reach a statistically relevant threshold. We use Visual Website Optimizer's duration calculator to help us predict how long a test will need to run (or if a test is even viable).
Depending on the number of unique sessions included in an A/B Test, we recommend allowing the test to run anywhere from a minimum of 2 weeks to a maximum of 3 months.