How old is the Universe?

Most scientists estimate the time between the Big Bang and current day somewhere between 13 and 20 billion years ago. Estimates are derived from Hubble’s Constant, a rate of expansion ratio calculated by dividing the speed at which a galaxy is moving away from the Earth by it’s distance from the Earth.

By taking the inverse of Hubble’s Constant (dividing the distance of the galaxy by its speed) we get an estimate of the age of the Universe. Of course, the distance of any galaxy and the speed at which it is moving are fairly difficult measurements to make and the uncertainty in these estimates lead to the uncertainty in the age of the Universe question.

Source and more detailed information: Wikipedia’s Age of the Universe entry.