The question was originally posed by Enrico Fermi, and has become known as the Fermi Paradox:
The extreme age of the universe and its vast number of stars suggest that extraterrestrial life should be common. Considering this with colleagues over lunch in 1950, the physicist Enrico Fermi is said to have asked: "Where are they?" Fermi questioned why, if a multitude of advanced extraterrestrial civilizations exist in the Milky Way galaxy, evidence such as probes, spacecraft or radio transmissions has not been found. The simple question "Where are they?" (alternatively, "Where is everybody?") is possibly apocryphal, but Fermi is widely credited with simplifying and clarifying the problem of the probability of extraterrestrial life.
A Danish researcher has come up with an interesting answer (if not a complete solution) to the Fermi Paradox:
...Which just means they haven't found us yet.
Extra-terrestrials have yet to find us because they haven't had enough time to look.
Using a computer simulation of our own galaxy, the Milky Way, Rasmus Bjork, a physicist at the Niels Bohr institute in Copenhagen, proposed that a single civilisation might build eight intergalactic probes and launch them on missions to search for life. Once on their way each probe would send out eight more mini-probes, which would head for the nearest stars and look for habitable planets.
Mr Bjork confined the probes to search only solar systems in what is called the "galactic habitable zone" of the Milky Way, where solar systems are close enough to the centre to have the right elements necessary to form rocky, life-sustaining planets, but are far enough out to avoid being struck by asteroids, seared by stars or frazzled by bursts of radiation.
He found that even if the alien ships could hurtle through space at a tenth of the speed of light, or 30,000km a second, - Nasa's current Cassini mission to Saturn is plodding along at 32km a second - it would take 10bn years, roughly half the age of the universe, to explore just 4% of the galaxy.