Similar to the folks above, I also had trouble with an HP Photosmart C7280 All-In-One after upgrading to Mavericks. Specifically, the fax printer no longer worked and re-adding the fax printer after resetting the printer system did not help.
With the help of the posts above, I found a link to manually download the ~500Mb "HP Printer Drivers v.2.16.1 for OS-X" Mavericks (http://support.apple.com/kb/DL907). For people with other printers, you might have luck finding a suitable download under http://support.apple.com/downloads/#printer
Prior to installing these, up I went into System Preferences -> Print & Scan and right clicked on an existing printer and selected "reset printing system", which removed all existing printers.
I then installed the manually downloaded printer drivers (took ~5-10 minutes).
After installing, in System Preferences -> Print & Scan, I added the fax printer by clicking + and then clikcing "Add printer or scanner...". After a brief wait, the fax printer then appeared in the list of available printers. Finally, I then added back the normal printer/scanner.
Since then, fax and normal printing are working fine.
I hope this can be of help to others,
Cheers, Grum.