I did the same, but was left staring at the message:

The Installer encountered an error that caused the installation to fail. Contact the software manufacturer for assistance.

Retrying the Installer, booting into Safe Mode and downloading the combo update all failed to work.
Delving a little deeper into the Console log files (found by opening Console.app from Applications/Utilities, clicking ‘Logs’ and the left hand side, then install.log) revealed that my install was failing due to the message

The operation couldn’t be completed. Too many open files in system


How could this be possible? The installer was the only thing running for me, and I had plenty of RAM and disk space, so what gives?
It turns out that – from this handy post – Snow Leopard only allows each process to have a maximum of 256 files open at any one time.

You can change the defaults (as shown in the link above) by typing this command into terminal:

launchctl limit maxfiles 1000000 1000000

This will set the max files per process to 1,000,000, which is more than enough.
Trying the installer again having entered this command into terminal worked perfectly!

Let me know if it fixes your problem.