We use the RAW version, meaning 1 is a failure and 20 is a success on attack rolls and saving throws.
In addition, we use the ´critical fumble deck´ from paizo, meaning when you roll a 1 you roll again, and if you miss, it becomes a critical fumble. You then pick a card from the deck and apply the result. The DM used to make up stuff before we had the deck without the confirm, but the deck introduces interesting effects that normally wouldn´t have come up, although the deck also tends to produce impossible outcomes, such as CON damage to an undead etc.
In one game, we also used a critical hit deck published by the same company instead of the standard critical hit rules, although I didn´t find that one as interesting to use.
I also remember playing another RPG, Cyberpunk, where the skill rolls where similar to d20, but you rolled a d10 instead.
However, when you rolled a 10, you got to add another dice to the result, without caps.
I managed to roll 2 10´s in a row once, ending up with a ridiculous score in the high 30´s I would otherwise never have gotten to!
I have considered using that as a replacement for the automatic hit of the 20 in the past, but have disgarded it because if would require additional dice to be rolled, and being redundant except when dealing with VERY high AC´s. (also, rolling a 20 means you don´t have to calculate what exact AC you hit. you just hit...)
