Mac shows desktop without menu bar or Dock after updating Snow Leopard
A few of things for you to try...

First, try starting in Safe Boot by holding the Shift key when you hear the startup chime. If you manage to successfully boot in this way and you can access the internet, download and install OS X 10.6.8 Combo Update V1.1. Restart and see what happens...

If that doesn't work - and you have the original discs that shipped with your Mac - start your Mac from disc 1, OS X Install Disc. Once it has started up find Disk Utility from the menu bar and select Repair Disk. When that has done select Repair Permissions. Finally, restart and see what happens...

If you installed from a retail copy of 10.6, follow the same steps above.

If you don't have the original discs, start your Mac and hold command + S to boot into single user mode. When it has booted you will see a command prompt, type in /sbin/fsck –fy, press the Enter key when done. A disk check will then be performed. When that's finished, type shutdown -r now at the command prompt. Wait for it to restart and see what happens...