For all that this is a common science fiction trope, it is highly unlikely.
First of all, procreation with an alien would probably be impossible. Even hybrids between earth species may or may not be fertile or semi-fertile (yes, I realize modern man bred with neanderthals, but these are two closely related species and a suspicious lack of Neanderthal markers on the Y chromosome indicate that it is possible such crosses produced fertile females and infertile males, as happens when small cats are crossed). An extraterrestrial might or might not use DNA. If they did not have DNA, then crossbreeding would be impossible. If they did, then it would still be unlikely to work without genetic engineering to combine it in a viable manner and even with that there would be a high chance of the resulting offspring being infertile.
As for actual mating - sexual desire is mediated by pheremones. While the alien with pheremones humans can't resist is another sci-fi trope (Orions and Deltans in Star Trek come to mind), it's also unlikely. More likely we would not respond in any way to each other's pheremones, making sexual attraction non-existent. Even that is assuming that the alien is not A. Physically incompatible and/or B. Hideously ugly to us and vice versa.
In other words, no...for purely biological reasons.