The first thing you should do, is go ahead and run the installation tool to do an uninstall. It probably will leave some things behind, but it's worth running. Then go through this list and remove anything it missed. This list is detailed enough though, that I believe even if you did not run the uninstallation tool, this would fully uninstall Oracle.
The most commonly missed item is to make sure you remove everything from the GAC because the uninstaller doesn't appear to. I get to that later, but if you wanted to know the largest source of uninstallation problems, it's libraries remaining in the GAC.
After running the supplied Oracle uninstallation utility (which may or may not do some or all of the following):
Look for any services with names starting with 'Oracle' and stop them.
Note that the services control panel will still show the old services until you reboot.
C:\Documents and Settings\All Users\Start Menu\Programs\Oracle*
Where * indicates the name of your install. Look for and remove all Oracle directories from that location.
Start->Settings->Control Panel->System->Advanced->Environment Variables
Edit both of the environment variables user PATH and system PATH. Remove any Oracle references in them.
There, now your system is Oracle free. If you are installing a new instance of Oracle (and not just an additional DB) I recommend you do this before any new Oracle installation.
Note: I used several other websites and searches as references when developing these steps, but I was unable to find any steps that covered all of the items for Oracle 10g so I assembled them here.