This is a big problem. The most common misconception about telescopes to the novice is that the purpose of a telescope is to magnify distant objects. While magnification is an important aspect of how a telescope works, it is not the primary function.
The main purpose of a telescope is to gather light and increase resolution of faint or distant objects. Practically any telescope can give you any magnification, depending on the combination of eyepieces and other augmentary lenses that are used. The problem is, most small "beginner" telescopes seen in department stores around the holidays are not capable of handling the amounts of magnification they advertise. They are usually 60mm diameter refracting telescopes which proudly proclaim "675x magnification!"
Here is one of the most basic rules when buying a telescope. NEVER BUY A TELESCOPE ADVERTISED BY THE MAGNIFICATION. While it may come with the lenses necessary to magnify that amount, the optics are so small and of such poor quality that you won't be able to see anything. In fact, the basic rule for figuring out maximum practical magnification is 50x or 60x PER INCH of aperture (diameter).
For example, one of those 60mm "holiday special" refractors can actually only (theoretically) provide good images up to about 120x. Usually this number is brought down even further by the scope being mounted on a wobbly tripod and having optics which are mediocre at the very best.
Most amateur astronomers will tell you that the best views come at lower magnifications on large objects like star clusters, nebulae and galaxies. The only time you really want to "crank up" the magnification is when lookign for minute detail on the moon and planets.
Remember: as magnification climbs, resolution and brightness dramatically decrease. Think about a TV set hooked up to a DVD player with "zoom" function. When you are watching a movie normally, the picture is fabulous. But as soon as you zoom in 4 times, the sharpness of a picture drops because the TV, the digital signal and the player were never meant to focus on such a small area of the picture at once with the same definition. The same is true with optics. The larger the aperture (or diameter) of a telescope is, the more you will be able to magnify the image in the eyepiece.
Also, you need to take into account that the more precisely made the optics are, the higher you can push the magnification. If you have a 16 inch telescope, but it has poorly made optics that are out of alignment, your image will break down at MUCH lower powers than a 4 inch telescope with pristine, well-aligned optics.