UPDATE: the 10.6.8 "supplemental update" (available via Software Update, in the Apple menu) fixes the problem. (7-25-2011)
The problem has been traced to a small change in the printing system. It appears to be a mistake. Fortunately, the fix is relatively easy. Just go to this web page: Mac users: After updating to 10.6.8, Getting “paused printer” message. FIXED! and download the Network Printer fix. Takes just a few seconds. Thanks to Eliran Sapir for the web page and the fix.
If your printer is connected with a USB cable don't worry, this issue won't affect you. But if you use a networked HP printer, or a networked Xerox, or a networked Canon or networked Minolta, or many others, you may run into the problem. The symptom is you try to print and right away the printer reports "paused" even though it is not. You won't make it work by resetting the printer system or reloading drivers or repairing permissions, so don't bother. Just use Eliran's fix. It only takes a minute and you'll be back in business.
UPDATE: the original link to the Network Printer fix application no longer works. Use this link instead.