Here are two images from the Hubble Deep Field Project.
According the the press release, the images each represent a region of the sky of a size which would be blocked out by a 1cm circle at a distance of about 25 meters (they actually say a U.S. dime at a distance of about 75 feet). Multiply the hundreds of galaxies in this tiny portion of the sky by the size of the entire sky and the result is a vast number of galaxies.
Specifically, if we assume that there are 300 galaxies in the first picture, then the math works out to 300 times the area of a sphere with a radius of 25 meters (i.e. 2500 centimeters) divided by the area of a circle with a radius of 0.5 centimeters. Assuming that there are 300 galaxies in the first picture and keeping in mind that the area of a sphere is given by the formula and the area of a circle is given by the formula , the number of galaxies in the sky is given by the formula or about 30,000,000,000 galaxies in the sky (MINSE was used to render these formulas).
Frankly, I have trouble believing that Earth is the only planet in all of these galaxies with intelligent life on it (assuming that there is intelligent life on Earth!).
The alternative (i.e. that we are alone) has always struck me as:
-Daniel Boulet (email@example.com)
Click on each image to get a much larger version.