Most versions of D&D don't offer a critical fumble rule. Some referees like to use critical fumbles in their campaigns. Rolemaster has a low percentage chance of a fumble (IIRC generally 3-8%, based on the weapon used). Some referees consider an analogous mechanic in D&D: A natural 1 is a fumble or other sort of critical failure.
But the typical critical fumble house rule (example here) is kind of lame...
Dropping one's weapon 5% of the time, injuring oneself 5% of the time, or stunning oneself 5% of the time seems more appropriate for Paranoia or Toon than it does for D&D.
This is especially true when someone has multiple attacks. Got three attacks? If so, you have more than 14% chance per round to negatively affect yourself in a round when you make all those attacks.
Furthermore, when odds of hitting in combat are low, a critical fumble rule pushes characters in the direction of not bothering to attack. Sure, maybe you're twice as likely to hit than you are to fumble, but the penalty associated with fumbling further detracts from the already slim odds of hitting, such that the combatant would be much better served doing something other than melee.
Contrasting with critical hits: As hit points go up, a critical hit (typical house rule: double damage or max damage) becomes less spectacular. The significance of a critical diminishes as targets increase in hp, because the critical is unlikely to materially affect the combat.
But a critical fumble stays equally jarring the whole time. An 13th level lord who drops his weapon every other combat looks pretty comical.
So what to do? Fumbles aren't unheard of in D&D's inspirational sources, so it would be nice to include them somehow. Here's an alternative:
Superior Fighters cause Foes to Fumble
In other words, a critical fumble rule becomes a class feature for Fighters:
If an enemy (with fewer hit dice, or optionally hit points) attacks a Fighter and rolls a natural 1, the superior skills of the Fighter has forced that enemy to fumble/drop his weapon.
There, that's better!