If you're getting black screens when you are using screen sharing in snow leopard, here's something that helped reduce (but did not completely eliminate) this problem for me. Basically, running the screen sharing app in 32-bit mode instead of 64-bit mode reduces the occurrences of the black screens.

To set the screen sharing app to run in 32-bit you need to edit the info for the app. Do this by opening a Finder window and going to /System/Library/CoreServices. Select the Screen Sharing then press the "More info..." button to see the info panel:

screen sharing info panel

You want to check the box next to "Open in 32-bit mode".

I found that doing this greatly reduced the number of times I got black screens when running screen sharing.