For Fighting Games, a similar 'thud' sound may occur, although in their case it's more often a Sound of Scratch Damage. This is common in Platform Games and Shoot Em Ups, and a high-pitched, metallic or hollow 'ping' is the most popular sound effect used, but a blunt 'thud' is also fairly common, and some games may opt for a deliberately humorous sound effect to mock the attacker. The Sound Of No Damage is largely associated with projectile weapons (think of that 'bullet ricochet' sound from any Old West film, for example), but can also occur with melee weapons - expect to hear this a lot when facing the Shield-Bearing Mook or if testing whether an element of the environment (like that cracked wall or oil barrel) really is or is not destructible. This is a case of Sound-Coded for Your Convenience (as a clue to stop wasting your attacks), and may involve Arcade Sounds.
And then there's a special sound effect used to warn that an attack has been repelled, blocked, or otherwise failed to affect the target. Most Video Games use one or two sound effects to punctuate the inflicting of damage against an enemy.