Connecting a camera to your telescope turns out to be rather easy. The only difficulty is actully creating some sort of physical connection. Fortunately there are any number of products to help with this.
As it turns out, different cameras work best for dfferent types of pictures. Taking pictures of bright objects such as the sun, moon or planets have their best results when taken with webcams. Deep sky objects, galaxies, nebula and star clusters are best with SLR cameras (or digital SLRs).
Compact digital cameras which can take movies are a pretty good median. They are better then webcams (but more expensive) for planets, however, although their deep sky object ability is usable, to get really great pictures you will want an SLR camera.
The picture of the thing above connects your camera (digital or SLR) to the eyepiece on the telescope. It is usable for compact cameras mostly. With SLRs you will want to use a T-Ring and a T-Ring adapter. The T-Ring physically connects your camera to the scope, essentially turning the telescpe into the lense of the camera.
Logitech QuickCam Pro 5000
So I did some research on webcams. It turns out that the best webcams use a CCD sensor instead of a CMOS sensor. The CCD is just better at picking up faint amounts of light.
Turns out the Logitech QCP 5000 is a CMOS sensor. The 4000 series was a CCD, however, when I went to buy one the store only had the 5000, which according to a website we looked at was CCD. Turns out the website was wrong. Unfortunately making a webcam compatible with a telescope requires some tinkering with it, thus the camera was unreturnable before I found out it was a CMOS.
Anyways, it is still usable and I have taken some interesting pictures with it but I will probably get a CCD one sometime in the future.
There is no shortage of digital SLRs out there. I choose a dSLR over a compact because of the sensor size. Compacts have way too much noise with to take long exposures. Plus most only allow up to 3 seconds, some up to 15 seconds, but a dSLR will allow you to keep the shutter open as long as you'd like.
Turns out that even at the highest ISO there is a little noise on the camera. However, I found out after purchasing this camera that Nikon's RAW image format isn't actually RAW. Nikon apparently runs all RAW photos though a filter to reduce noise. This is pretty bad for taking picures of the sky, since very fine focused stars will be deleted because the camera will think that they are just common noise. There are ways around this, however, though they are not easy to automate over a long photo session.
At any rate, in practice this filtering does not seem to be a problem.
I choose the Nikon over Canons since the Nikon was a CCD and the Canons were CMOS. I don't know how much a difference that makes with SLRs as it apparently makes a big difference with webcams. That was the main reason for the Nikon over the Canon.
As it turns out all cameras come with a built in hydrogen filter that makes taking pictures of nebula a bit difficult. A lot of light gets blocked from nebula so they don't come out as bright as they could. For a couple thousand dollars you can get a modified dSLR which has this filter removed, but then it can't be used for normal photography. If I happen to stumble across $2000 or rob a bank in the near future I may pick up a camera specifically for astrophotography.
My recommendation: If you are getting a dSLR then go with something that you will use day to day and just live with any difficulties your particular camera may have when it comes to astrophotography. If you have a tonn of extra cash laying around and are really into astrophotography then do some research and purchase the top of the line modified camera for astrophotography at the time.