If sex is prohibited, how do we survive? Sex can lead us to suffering in many ways; however, if all of us are just like Lord Buddha according to his story, wouldn't humanity become extinct?
Sex is prohibited for monks and nuns

If you are not observing higher precept like 8 or 10 precepts sex is not prohibited for lay person. Lay person has only to adhere to 5 Precepts. This prohibits wrongful sexual acts, i.e., sex with someone under another's protection... and other acts.

As you said sex is craving and can lead to suffering. But not very body or householder is in the stage to eradicate higher stages of craving for sensual pleasure than the rudimentary level which might lead to misconduct. At the basic level this is what is required. As you progress in the path you have to remove sexual urge.

Also Vipassana Meditation can help reduce sexual urge. There are Samatha techniques also but if you take the insight root you kill 2 birds with one stone. You can try http://dhamma.org or http://internationalmeditationcentre.org which has centres in many cities and faily large outreach.

You loose complete sensual desire is when you become a non-returner where by you eliminate the fetter of sexual desire. If you take human world number of being achieving this state is small. Hence there is no risk of extinction. Also a stream enter will have lust and a lay follower may engage in sex as long as it is lawful (a stream enter does not engage in sexual misconduct).