Critical Successes are fairly ubquitous in RPGs, but critical failures, or botches, seem to be more optional. Not every game has them, and those that do have different degrees of it. A natural 20 is often an auto-hit plus additional damage, but a natural 1 might just be an automatic miss without anything else. In another game that same 1 may mean that not only do you miss but some additional bad thing comes to pass.
Does your game use critical failures or automisses? If not, did you add them in? If not, what about critical successes? For that matter, what game is it you're playing and how does it resolve dice rolls?
L5R doesn't have any mechanical critical successes in it, aside from the ones players call for themselves with raises. Roll and Keep works by making a dice pool out of your trait and skill, then rolling them and adding up a number of dice equal to your trait. This gives you your total roll. It makes for a neat balance between skill value and ability value and works fairly well.
Esteren has both critical successes and failures. The dice system works by rolling a single D10 and adding your character's Way (basically an attribute) and skill rating. Higher the roll, better it is.
Star Wars by Fantasy Flight Games doesn't have Critical Successes and Failures, but it does have Triumphs and Despairs. I say these are different because you can get a Triumph without succeeding. You can also get a despair without a failure. As for how it works: you make a dice pool again based off trait and skill, but also off the difficulty for the roll and other environmental details. You then add up your successes, failures, threats, advantages, despairs, and triumphs and see what comes out of it. It works out well, better than it sounds.
What about your game?