Well, that's actually a more complicated question than one might expect. Many people, when they ask this question, want to know how many times an image is magnified when you view it through the telescope, as compared to when you view it with your naked eye. If this is what you're interested in, the magnification can range from 122.2x with our 32mm eyepiece, to over 400x with our 8mm eyepiece. However, the eyepieces generally used for public and private sessions give 122.2x (32mm) and 78x (50mm) magnification.
For astronomers, however, magnification is less important than light gathering power. The more light a telescope can gather, the fainter the objects that one can view with it. Magnification is nice, it makes it easier to see details of objects, but without sufficient light gathering power, the nebulae, and galaxies that we're interested in observing, will be too faint to see.
The light gathering power of a telescope is determined by the diameter of its primary or objective mirror. Telescopes are basically light buckets, the wider they are in diameter, the more light they can collect, and therefore the fainter the objects are that we'll be able to see. Our telescope is 14 inches (355 mm) in diameter. As the light leaves the telescope's eyepiece at the spot where the image comes into focus (known as the exit pupil), it is about 7 mm in diameter, so the telescope's primary mirror is about 50 times wider (350mm/7mm) than the exit pupil. That means that the mirror has 2500 times more surface area than the exit pupil (50 x 50). So, using our 14 inch telescope, we'll be able see objects that are 2500 times fainter than we would with our naked eye. This means that we should be able to use this telescope to see objects that are about 14th magnitude.
Magnitude is a measure of how bright a star appears when seen from Earth. It is related to how much energy is leaving the star as visible light and to how far the star is away from Earth. The smaller the magnitude, the brighter the star. The brightest star in the sky other than the Sun is Sirius, which appears to be -1 magnitude. The faintest stars that a human eye can see on the clearest night are 6th magnitude; there are thus 7 magnitudes between them. The stars at the limit for observing through our telescope are thus slightly fainter compared to the faintest ones we can see as those stars are to Sirius.
This assumes though, that we are looking through a vacuum, which we are not. Air currents in the atmosphere and scattered light from street lamps, nearby cities, and sometimes the moon, brighten the background of the sky and limit how faint the objects are which we will be able to see. Since we are fairly close to sea level, there's a lot of atmosphere and moisture to look through, and since we're on campus, albeit at the edge, there's a significant amount of light from nearby buildings and street lamps as well. I usually have success with spotting objects which are brighter than 8.5th magnitude and have been able to spot on occasion objects nearly as dim as 10th. Since the light from these objects, usually nebulae or galaxies, is spread out and not concentrated at a point, like a star, I expect that the dimmest stars that I see on those nights are between 10th and 12th magnitude. The Keck telescopes in Hawaii, which are 10 meters in diameter, can detect stars at about 22nd or 23rd magnitude.
The UNH Physics department uses this obsesrvatory strictly for educational purposes. In addition to the public and private viewing session that we offer, students in PHYS 405/406- Introduction to Modern Astronomy, and of the introductory astrophysics class are brought out to the observatory at least once a term (there are many sections, so this can take the entire term). Students in the introductory class then must write a laboratory report about the telescope and the objects that they see.
While it might be possible to do some rudimentary research with a telescope this size, these days it is more of a 'scope for a dedicated amateur. Such amateur astronomers are noted for spotting new comets and asteroids. The High Energy Astrophysics Group research group here does do astrophysical research, but uses a telescope (COMPTEL) on an orbiting satellite - the Gamma Ray Observatory. Unlike the Hubble Space Telescope, COMPTEL looks at light that is of much higher energy, and therefore of much higher frequency than we can see directly with our eyes.