You see extra damage is nice and in games with hit points that can be a big deal, but other than bigger numbers that doesn't make what should be a special moment special at all. In the example I gave I talked about the Serious Wounds table the D&D 5th Edition has in their DMG. Since I don't want to risk angering the WoTC gods by some chance I'm not going to post it though. Basically it's a D20 table that ranges from a minor scar that has no mechanical effect but it still a lasting reminder all the way to losing a hand foot or eye. What I don't like about it is that as I said in my other article these outcomes are nearly the exact same chance. I would want losing a hand my chances to be grievously rare and I'm sorry but simply rolling a 20 (or even lower with certain fighters) is not that rare once you get deep into a campaign and even worse what if this happens due to jsut some lowly goblin with a dagger, that's just insulting.
To try and remedy this I cooked up a couple alternatives. The first it just another table, but it's a 2d6 table meaning that sweet bell curve is involved to control the more dastardly outcomes, but they are still chance which doesn't fix our pesky goblin issue. The other is based off of the Concentration mechanic already in the game and thus scales based on how much damage is dealt to the character. This means low threat enemies won't be able to chop off limbs, but it does involve a bit of math.
Finally since the first system is pure random I add the caveat that when a crit is rolled you then roll another d20 on a 10-20 it's just a crit (HA just a crit) but a 1-9 rolls on the table. This makes these wounds just a bit more special than simply getting a lucky roll (you need TWO lucky rolls). The second table uses a save so it's actually tied to the characters ability to avoid the wound.
First up the 2d6 Weapons Critical Table
This on I had planned to do a separate table for magic attacks, but I ended up moving on to the other table after a player suggested tying the whole system to character ability and damage dealt.
Second the Wound Save Chart
For this version of crits I also added a special feat players can take
Gain +1 Dexterity and can use Dexterity in place of Constitution for saves against critical hits.
In both cases as I don't tend to have many actual dungeons in my games and combat can easily only be once per day I'm adding this special setting rule. Even if you are using the standard Serious Wounds or any other crit mechanic other than just the extra damage this rule could work in your game.
Heroic Crit Save:
Any time a character with class levels is hit with critical damage they can spend a hit dice to to (Either roll on the critical table or save against a critical wound). This must be done before any additional effects are rolled for.
If it isn't obvious I'm going with the second option personally, but feel free to borrow or improve any of these for your own game.