I like the idea behind critical strikes; they make combat a little more exciting for players. Finding the right balance, mechanically, however, takes some thought. I'm not a fan of auto-kill because that can ruin the fun too easily. Nor do I like maximum roll damage because that could happen anyway. I want the critical strike to be an exciting above average strike, but not a game changer. What I've settled on is a natural roll of 20 is a critical strike that does maximum damage plus one damage roll. For example, a d6 sword, on a critical strike does 7-12 (6+1d6) damage and a d4 dagger would do 5-8 (4+1d4). This will be appropriate with both lower and higher level characters because, presumably, the advanced players will have high damage weapons.
The Red DM mentions that a downfall of crits on a natural 20 is that it "isn't influenced at all by the AC of the target". If the d20 to-hit roll includes (philosophically), not only the physical aspects of combat, but the strategy and other cognitive aspects, we can allege that the critical strike is exceptional planning or battle strategy such as feinting, high/low combinations, exploiting the environment, etc. Or, we can just say a character got lucky.
Inversely, I also like the idea of a critical fumble to balance out the critical strike. It isn't essential, but I like the the dichotomy and tension it brings to the players. Finding the proper balance of increasing immersive fun without killing a character is equally difficult. Zero damage isn't enough, and self-inflicted damage can cause significant player anger, so I go with player loses one turn on a natural roll of one (critical fumble). This can be seen as a trip, or really bad attack strategy.