Hi Cam. I have the same printer on a MacBook Pro and have been struggling for the past 24 hours to get it to print & scan, having loaded Leopard over the weekend. I don't think that you're going to able to scan using the 6180 until HP provides an updated driver set for Leopard (in my experience, the underlying applications like Adobe 8.0 or Preview will crash before they can save a scanned document). However, you should be able to get the 6810 to print.
Everyone's system is configured differently but here's what worked for me; uninstall the HP software including any instances of HP software that you find in your hard drive - to do this, go to your Hard Drive in Finder and select Library. Scroll down to Printers and remove any HP folders that you find (not just references to your 6180 - any and all HP folders). Then back in Library, scroll to Receipts and remove any HP folders that you find. Close out and go to System Preferences and then go to "Print and Fax". Remove any HP printers in the menu using the "-" key below the printer selection.
Now, go to Applications and then Utilities. Click on Disk Utility and select your Hard Drive. Click on "Repair Disk Permissions" and let the program work its magic. When it's finished, close out of the program and reinstall the HP software which you can get from HP (it's important that you use version 9.5 of the HP driver set which is the most current version available on the HP website). This runs version 1.3.1 of the HP Device Manager and this is what you should be loading.
I'm assuming that you want to use the printer wirelessly - if so, don't bother connecting the printer to your Mac, Bonjour will find it. After you've downloaded the driver set, launch and install it. When it's finished installing, it will launch a wizard to configure the 6180 for your computer. It will ask you to click on the "Print Utility" - Leopard doesn't have one so don't bother to click on this icon! Before you go any further on the wizard, go to System Preferences and click on Print & Fax. Click on the "+" key to add a printer. Give it 60 seconds to find the printer - it will offer you both the "HP6180" and the "Photosmart C6180" printers. I would add both but I would make HP6180 the default printer.
When you've added the printers, go back to the Wizard and let it finish what it started. When you're done, you can go to the HP Device Manager (you'll find it in your Dock) and click on the "Information and Settings" tab at the bottom. Scroll down to Maintain Printer; if you don't see your printer, click on More Printers and add HP6180 when it appears on the screen.
That's it. I hope it works for you and others, like it has for me. I can print now but I can't scan - this is exactly what happened to me when I upgraded to an Intel Mac - it took HP months before they updated their drivers for the system but they eventually did. I suspect that the new drivers will appear much faster with Leopard since the installed base is rising rapidly and is a more important source of revenue for HP.
If you use Adobe and want to add Adobe to your printer set, here is what worked for me. Open Adobe (I have 8.0 Professional) and go to "Check for Updates" in the help menu. If there is one for your version, make sure to close out of all your open applications (especially Acrobat) before you launch the update. When finished, open up the application again and go back to the Help menu and scroll down to "Repair Acrobat installation". Make sure to check the box only for the "Adobe PDF Printer" - the other two items should be left unchecked. The process will take a couple of seconds and you can go to System Preferences and open up Printers and Fax - you should see it there as a new printer. I would make sure to check "Share this Printer" for all 3 printers that appear on the menu, in the event that others devices might be using them.
Good luck!