Contact Damage

[Kriven]

It depends on the game... Koopas shouldn't ever have to punch Mario to hurt him (Super Smash Bros. aside).

To be honest, I've been screwed over more by games with attack animations that don't line up with their hitboxes than games with contact damage. At least in the games with contact damage you're conditioned from the get-go to approach combat in a specific manner, games with poor attack animations are often confusing and frustrating. Particularly when you have instances where the enemy objects don't have any knockback and just keep going through their attack animation while the hero character is finishing up his.