There is no definite answer to this question since every person is different. Some people may have an addictive personality and the cravings might last for years. Other people may not experience any desire to smoke almost immediately after taking the final step to quit. A helpful point to keep in mind is that you have quit when you finish each cigarette. The decision to smoke or not to smoke again is entirely up to you. Also, keep in mind that a period of 3 weeks is a typical time period for a habit to be made or broken, so if you are able to make it past 3 weeks, you have a much higher chance of not smoking again.
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