To trash Classic:
1. Backup your data in case you make a mistake.
2. Make sure no Application in Applications Mac OS 9 folder lists itself in Get Info as an Application (as opposed to Classic Application). Any that are just plain Applications are designed to run natively in both Mac OS 9 and Mac OS X and can be moved to the Applications folder, assuming they didn't install special components that required them to stay in the Applications Mac OS 9 folder to work.
3. Drag both the Applications Mac OS 9 and the System Folder (containing the Control Panels and Apple Menu Items folder) into the trash. Do NOT trash the folder named System which belongs to Mac OS X.
4. Secure Empty Trash from the Finder File menu. If that takes too long, you can use http://www.macosxcocktail.com/ 's software Cocktail. This software is kind of a swiss army knife, and should only be used for specific functions when needed. Ask before using a utility within it, if you are unsure how it might affect your system.
5. Verify all the applications you use work.