It occurred to me that in any system that has critical hits, they are immensely popular.  Besides the obvious "Your attack is super effective" bit, I think they have a lot of subtle reasons for being popular as well. Now, with some of the recent discussions here, an idea sparked in my mind and it just took hold.  How about a mechanic, that once you roll a "Critical hit", you and your opponent do several roll offs, until a predetermined situation?

Lets use D&D 3.5 for example.
You roll a critical hit, and you roll damage like normal.  You then have your critical damage (lets say this is just 1d12 or something.)  Your opponent also has a "fortification score" or some such thing (based off of armor?)  Lets say his fortification score is 1d10. 
Then, the attacking player rolls his damage, and the defender rolls his fortification score, until the defender has the higher number. So, to further the example...
Attacker rolls 7, defender rolls 4
Attacker rolls 11, defender rolls 9
Attacker rolls 2, defender rolls 5 (the critical hit stops.) 

The attacker's critical hit deals an additional (7+11+2) 20 damage! 

Now, I think D&D would be a poor candidate for this, as combat already is tedious. I don't think it'd fit in my current project either, but I can imagine it working well in a simplified system that focuses on player achievement in combat.  What do you guys think? 

While I do agree that critical hits probably have other reasons for being cool (such as they feel like you've achieved something special even though it was really just luck) I'm not sure if this would really help anything. It's an interesting idea on its face- a critical hit triggering a little mini-game- but the way you outlined it it just seems like extra reward for little effect (and actually, it might make things less fun, like say if you failed on your first roll and did only 1 extra damage or something. Still, I think the idea does have a lot of potential.

It's a great idea, I love the mini-game thing involved but it clearly sets some frame as well, it emphasizes set values over luck. What people love about crits is the chance they offer to shine in situations they wouldn't otherwise. Your system sort of cuts that. Another crit system I've found in Moongoose OGL Slane piles up the crits until you enter a state of pure fury with cool random effetcs tables. The open-ended crit thinking is definitly something the players look for, but it often gives the same chances to their foes, which is no good news for them. In Slane that's covered the easy way: Most of the time, only the PCs have access to this.