This glitch may not work depending on the version of Super Smash Bros. Melee you own
Go to Training Mode as any character, and any level. Press start and highlight "reset", but don't press it. Now, fall off the ledge, or make your character commit suicide. While he's dying, hit start and press A to choose "reset". If you timed it correctly, your character will come back to life with no damage counter. So, getting injured doesn't affect you at all. If you die again, your damage counter will return, unless you hit reset again.
Submitted by: Jesse