The 'Windows only' HP Laserjet budget range of printers, such as the 1000 and 1020, use ZjStream protocol rather than the more usual PCL or PS supported by OSX.
For Tiger and previous OS's, the generic 'SDK Mono driver' could be downloaded from Zenographics website and used to support printing direct from Mac OSX to the 'Windows' printer. This was especially useful where a Mac is used in a predominantly Windows-hosted network which has shared HP 1000/1020 printers.
There are many reports that the 'SDK Mono' driver does not work after upgrading to Leopard, due to underlying changes in the CUPS software. Unfortunately, Zenographics no longer support that driver since they merged into the Marvell business.
The solution is to uninstall the existing 'SDK Mono' printer, and install the OSX port of the Linux freeware foo2zjs package. This converts the print data into ZjStream format and sends it to the HP printer. After installing foo2zjs, reinstall the printer again, and select the 'HP LaserJet 1020 Foomatic/foo2zjs' driver.
Download here:
http://www.linux-foundation.org/en/OpenPrinting/MacOSX/foo2zjs
Be sure to install all 3 packages in the following order: espgs-7.07.1.ppc.dmg, Foomatic-RIP, foo2zjs-1.0.U.dmg. The final package will prompt you with some important firmware information; you can ignore this if the printer is physically connected to Windows PC, as that PC will take care of loading the required firmware at startup.
I just tried this on Leopard and it's printing correctly to my HP 1020 shared on a Windows 2000 PC.