Theories/Speculation
One NASA estimate suggested that there were, in the observable universe, a sextillion stars (1 followed by 21 zeroes). And while a later estimate revised that number to 70 sextillion, even professional astronomers aren't convinced of their own estimates. Furthermore, even these numbers come with a caveat: They are only an estimate for the number of stars in the observable universe--those stars within range of Earth's telescopes, including the mighty Hubble.
Size
Not even professional scientists know how big the universe truly is. Although as many as 8,000 stars can be seen from the earth with the naked eye (at best), the observable universe extends at least 93 billion light years across. And yet, the universe may extend much farther than any of our technology can observe. Without knowing where the universe begins and ends--if it even does--there is no way to accurately gauge the number of stars in the entire universe.
Misconceptions
There is presently no foolproof way to determine the number of stars in the universe. At best, the only way to gauge the total number of stars is to estimate the number in one infinitesimally small patch of sky, and then to extrapolate that estimate to the whole universe. With the universe as large as it is--perhaps infinitely large--a specific number may prove to be forever out of reach.
Considerations
Many factors prohibit the accurate estimate of the number of stars in the universe. When it comes to estimating a certain patch of sky, modern telescopes can only see so far, and the thick layer of the earth's atmosphere prevents a clear picture of even that. Although the Hubble telescope is capable of detecting about 80 billion galaxies, there's very little way of knowing how many galaxies exist that are too faint even for the Hubble. The universe, meanwhile, is not a static entity. Stars live and die throughout the universe, and will continue to do so.
Potential
As of 2008, the deepest image of the universe ever taken--the Hubble Ultra Deep Field--contains an estimated 10,000 galaxies. From the perspective of the earth, these galaxies all reside in one thirteen-millionth of the total area of the sky. As deeper and deeper images of the universe are taken, and as constants and models are further refined, scientists may be able to venture more and more accurate estimates of the stars in the known universe.