The claim that NASA has asked people to have sex in space as a scientific experiment seems a bit far-fetched to me. I would expect them to experiment with animal mating first, which it doesn't seem they have done. (Update: Russia experimented with gecko mating in July 2014. The experiment was not successful.)
As for whether or not any sex-in-space has happened, that is harder to say. No one has publicly admitted to it, but that doesn't mean it hasn't happened. There is this article in which an astronaut provides an adamant "no": No Time for Sex In Space, Astronaut Says. But that doesn't prove that it has never happened either. ("He's just jealous!") Astronauts are human and may give in to their emotions at times. You may recall that there was once an astronaut who put on astronaut diapers and drove a thousand miles to try to kill another astronaut's girlfriend. So you can take any notion that they are completely professional all the time, and throw it out of the airlock.
There is also this:
The first married couple to fly in space together were N. Jan Davis and Mark C. Lee who both served as mission specialists aboard Endeavour on STS-47 in September 1992. Lee and Davis had met during training for the flight and had married in secret. They disclosed their marriage to NASA shortly before the flight, when it was too late to train a substitute. NASA has since changed the rules and will not allow married astronauts on the same flight.
Source: Wikipedia (sourcing CNN)
Of course, they've never come out and said that they had sex while they were newlyweds in space.
Update: It looks like there may soon be a definitive "yes", as there are now plans to film an adult movie in space.