In this post, I'll address photography with beginner telescopes, that is, those without a right ascension driver (RA drive). A little divergence here, what the heck is a RA drive? First off, right ascension, if you you stand in your favorite celestial viewing area and face north (toward polaris), and turn to your right (east), then that is the direction that the celestial objects ascend into the sky, thus the term, right ascension. Beginner telescopes typically are refractor type (objective lens in the front, eyepiece in the back) or reflector (mirror in the back, eyepiece in the front) and are stationary on a tripod, i.e. they don't have a right ascension drive. Now that we have that out of the way, what can you photograph with your telescope? Fortunately, depending on the magnification your telescope can achieve, lots!
There are generally speaking two types of photography with a telescope, prime focus and eyepiece projection. 
With prime focus, you essentially take the eyepiece out and mount the camera directly to the telescope. In the photo on the left, you can see one of my typical setups. In this instance, I'm shooting three cameras at once, but the one of interest is the scope (refractor) on top, note the camera mounted directly to the telescope. This is done with a readily available part called a t-mount. It's fitted to your brand of camera, I use olympus and canon cameras, so the t-mounts I use fit the bayonet mounts of these two camera types. T-mounts are readily available at all online telescope vendors (anacortes, adirondack video astronomy, optec, etc...) and locally at Rivers photography in Dover, NH. Once you have the t-mount, all you need is a shutter release cable and a t-mount to focuser adapter. Most telescopes have a 2" or 1.25" focuser, so you'll need an adapter to screw mount the t-mount to your scope, once you do this, hook up the camera to your telescope, point it at the moon, and shoot! Here's one I took in Apr '06 of the crescent moon using this method:
I liked this photo because the part of the moon not illuminated by the sun is still quite visible, this phenomenon is called earthshine. If you get the proper filtration for your scope, then you can also photograph the sun. Here in the northeast we had the pleasure of having a nice cloudless day on June 8th 2004 to view the first time in any of our lives that venus passed between the earth and the sun, using a small refractor, a nikon coolpix 4500 and a thousand oaks solar filter, I took this picture.
This same method can be used to photograph a solar eclipse, although the last really good one here in New England was in may 1994, well before my first venture into astrophotography (although I did try photographing it with a film camera and three pairs of sunglasses for filtration, needless to say, this didn't come out).
Eyepiece projection
The other very useful technique for solar system photography is called eyepiece projection, using this method, you can either hold the camera right up to the eyepiece and shoot (and some people get some amazing results) or you can use a similiar method as described above where you buy a tele-extender and the t-mount, and you put the eypiece in the tele-extender, mount the camera to the tele-extender via t-mount, put the tele-extender in the eyepiece holder (typically called a diagonal) and shoot. Because this is a setup prone to vibration, best to use a shutter release cable. The advantage to this technique is that you can get much more magnification. Using this technique, as well as a technique called averaging (where you take multiple photos and use an application such as registax to layer them together), you can get some really nice results, here are some examples of eyepiece projection:
Solar system objects are bright enough that they really don't require long exposures, typically about 1/16th to 1/8th of a second, but bracketing your exposures is best, especially if going with a digital camera. One thing I haven't touched on much thus yet is focusing, it becomes challenging with dimmer objects, but with bright objects such as the moon and planets, it's not much of an issue.
john
Here in this Hubble photograph you can see the fragments trailing the primary. Will this comet make it past Earth before completely falling apart? Wait and see! For those of you worried about impact, nothing to worry about, this whole shroud of comet matter will pass about six times further than the moon to us. The whole story can be found here: http://dsc.discovery.com/news/briefs/20060501/comet_spa.html 
