Most of your typical point and shoot camera won't work that well. They will do planets and the moon OK but not much else. It's harder to focus, the sensors usually don't work too well at high ISOs and the inability to change lenses is one of the biggest problems. Overall they just aren't suited for astrophotography as well as a film camera, or DSLR.
I would strongly suggest finding a Digital SLR if you can afford it. I have a Canon Digital Rebel. You can find some great deals on Ebay. They are down to a few hundred dollars.

However if you can't get a DSLR then you can go here for adapters.

Agree with the other poster. I would add that you would really want to have a clock drive and a drive corrector on your telescope and a bulb setting for the shutter speed on the camera. This allows you to hold the shutter open for very long periods of time and makes it easier to bracket exposures for the best results. I have a Canon 20D and I use only the body, not any lenses. I project directly onto the CCD from the eyepiece.

[edited]
I am learning to use Canon 40D, and find I have the following problems:
1) Mount jiggle / wind / footsteps near my telescope mess up my photos.
2) Focussing is real pain, since the light level is too low for the camera to show on the screen, and the viewfinder is too small to properly focus. I have to use a guide star to check focus, then slew back. Then maybe the viewfinder shows one or two stars when at 1600 ISO. Get a backup plan for focussing, like parfocal setup i.e. you can setup without cam, and just attach it without having to change anything.

(see first answer) You can get what is probably a 58mm adapter from Canon or Scopetronics and others, $19. Then add the step ring to get to t-thread, $31. A digi-t allows you to attach 58mm to existing eyepieces directly, for $60.

You also don't have RAW format capability, unless you use the hacks available on the internet, check CHDK. RAWs help you get the most of your CCD.

You are limited to 15 seconds exposure. This is not enough for nebulas, and makes using O3/SII/Ha/Hb filters almost out of the question because the image will be too dark. I am finding that I get good pictures with 30-500 seconds on 40D.

Another alternative to on-axis is to get a clamp around the scope that gives you a mounting 1/4-20 thread that holds your camera. Disadvantage of this is:
a) You have to deal with the chromatic aberration (color shifts) of your S3's built in lenses
b) You probably have to use the optical zoom feature at to get rod of the vignetting (camera CCD too large / too far from eyepiece). Scopetronics has a solution to this. It wasn't too bad for my G7 (25mm CCD) and 50mm eyepiece, but most scopes have much smaller eyepieces. Or you can spend more money on a 0.66x reducer lens, may help as well.
c) You need to align the camera precisely to point in 3 axis at the center of the eyepiece. Off by a mm, and you won't get everything. Then you have to be aligned in the axis of the scope. Remove the camera to look in the eyepiece, and you may have to do the alignment again.
d) You may need to make your camera do manual focus, because most cam's cannot smell -5 mag light. My G7 needed to be in Manual+Macro mode, at around ~20cm focus to work, to shoot the moon.

With the above G7 setup, great moon shots, except for the yellow/blue shift.

A real advantage of the pocket cams are the ability to do video. If you can snag Saturn, and keep it centered, you can use 1/60 or so video, and stack that. Apparently

Well the others are right, but I think I have something to add since coincidentally I use the Canon Powershot S3IS for all of my photography (astrophotography included).

I have an S3 and an adapter from scopetronix.

There are two options for the adapter from scopetronix. First for about 100 bucks you can get an adapter that will work with any 1.25" eyepiece that has a removable eyeguard.

For 200 bucks you get an adapter that comes with a special 40mm plossl eyepiece. That is what I bought.

I didn't want to buy a special camera, or a camera that costs more than my scope. I just wanted to use the camera I already had. People tell me all the time that a DSLR would work better and take better quality pictures. Well obviously a 1,000 dollar camera should take better pictures than a 300 dollar camera. That kind of goes without saying.

Now the main question is what do you want to take pictures of?

If you want to take pics of the Moon you can probably accomplish that with just about any digital camera. I took this picture without an adapter by just pointing my camera through the eyepiece of my tele………
100X magnification.

If you want to take pictures of something other than the Moon such as Saturn or Jupiter your telescope will need to be tracking these objects. If your telescope is not tracking then forget about it.

Now there is the question of deep space photography. Any decent pictures you see of deep space are usually long exposure shots. The longest available exposure on the S3 is 15 seconds!! Not very long. You can always stack photos but I am not into that. A picture to me should be a snapshot of what I am seeing. A photgraph should be a reminder of what I once saw. Long exposure shots(false color), and stacked images look pretty, but they do not represent what we see.

Long story short if I could start over or afford a different camera I would definitely do so. Don't get me wrong this camera kicks some serious butt . It just doesn't seem to be a great choice for astrophotography……I am just an amateur, and I am totally happy with the pictures I have taken, but if you want professional quality astrophotos you will have to consider other options.

Some more of my pictures…….http://farm3.static.flickr.com/2099/2127874358_16c59444f7_b.jpg

50X magnification