There's been a lot of discussion on how critical hits should be handled in DnD Next, along with a lot of criticism on how they're currently mentioned in the playtest packet. So I decided to share my thoughts on the topic, offering my own personal preferences and suggestions for this highly subjective game mechanic.
Why So Critical?
First off, what should the designers' goals be for a good critical hit mechanic? Here's the criteria I used for mine:
Design Objectives:
1. Must be fun. First and foremost, the mechanic must be fun to use above all else.
2. Must be rewarding. Players should feel like something epic happened.
3. Must be easy to use without a lot of number crunching or +/- modifiers.
4. Should be realistic enough so as not to seem impossible.
Trigger Methods
Ok. We've got our design goals. Now we must decide what triggers a critical hit. Below are some of the most popular methods. There are others, but these are the best of the best...of the best.
Method I - "Natural 20"
With this method, a critical hit is triggered when the player rolls a natural, unmodified 20 on an attack roll.
The Good:
1. It's traditional and easy to recognize. Everybody knows that a natural 20 is a good thing when attacking. It's been a part of the D&D game since the beginning, even though it wasn't officially adopted until 2e.
2. It's simple and fast, requiring no number crunching.
3. It's comfortably rare. There's a 5% chance of rolling a natural 20...that's a perfect probability to work with considering a critical hit is supposed to be something special.
The Bad:
1. It eventually becomes apparent that the only way for lower level characters to hit higher level monsters is with a natural 20. That's a problem for obvious reasons.
2. Not very realistic.
Method II - "Level of Success"
With this method, a critical hit is triggered when you roll higher than the target's AC by an arbitrary number (usually 5 or more higher than the AC).
The Good:
1. Provides a sense of difficulty scaling; that is, the higher the target's AC, the more difficult they are to score a critical hit against.
2. Takes skill into consideration. Skilled combatants are more likely to score critical hits, since they are more likely to roll higher than their target's AC.
The Bad:
1. Adds an additional element of number-crunching to the attack roll to determine if a critical hit is scored.
2. It triggers more frequently during combat, especially against targets with lower AC. This can slow combat down depending on how you resolve critical damage (see below) and it also makes critical hits less special.
The Ugly:
1. It lacks that level of excitement that a natural 20 commands when it comes up during battle. Whether a real or perceived issue, it's an issue (for me anyway).
The Verdict: Method I
Both have their strengths and weaknesses, but for our design goals, Method I fits better. Method II works fine and it's a bit more realistic, but it's not as much fun or as easy to use as the Natural 20 method.
Ok. So Natural 20 comes out ahead marginally, but it still has a few drawbacks. How can we fix these and improve upon the mechanic?
Well, there's...
Method III - "Confirmed Critical"
DnD 3e introduced this method (with mixed reception) based on Method I. When a character scores a natural 20 (or sometimes 19 and/or 18) on an attack, they make another attack roll. If that attack hits, then the attack is a critical hit. Otherwise, it's just a normal hit.
What does this bring to the table and why is this a better way of handling critical hits than Method I?
1. Takes skill into consideration. The second attack roll verifies whether the attacker has the enough skill to hit his target normally or if it was just a fluke.
2. Eliminates the problem of lower level characters only being able to hit higher level monsters with a critical hit.
3. Provides a sense of difficulty scaling; that is, the higher the target's AC, the more difficult they are to score a critical hit against.
4. Adds realism, without adding number crunching.
So...it basically gets rid of the bad stuff from Method I and adds all the good stuff from Method II? Sounds awesome. Any drawbacks?
Of course...
1. An extra attack roll is required if triggered.
2. Makes critical hits exceedingly rare, and it can be a disappointing let-down after getting a natural 20 only to miss an easy confirmation attack roll afterward.
The Perfect Method
Ok. So...none of these methods are perfect. Now what?
Here's where personal preference on the matter really kicks in the most. The payload method used for the critical hit, can really make a difference on what trigger method is best suited for your campaign.
For example, I really, really like the simplicity of Method I and think it works quite well under most circumstances, but it's drawbacks can become kind of silly at times.
I've used variations of Method II for many years, and it works very well for other d20 game systems with a focus on realism, but it's not quite suited for a casual D&D game.
I eventually conceded to Method III shortly after 3e...It just makes sense on a lot of levels and I'll explain why below.
Payload Methods: Critical Damage
No matter what trigger method you use, it's time to decide what the payload is. That is, now that you scored a critical hit, what happens next? Well, let's look at the most popular payloads:
Double Damage
A classic payload that dates back as far I can remember...and that's a long time. With this method, you do whatever damage you would normally do on an attack (after ALL bonuses, modifiers, multipliers, etc. are applied) then double it. So, if you did 15 points of damage after all modifiers and bonuses, your total damage would be 30. It has a tendency to cause confusion when other multipliers are involved, and often arguments ensue about which multipliers are applied first. I've always treated the critical hit multiplier as the last word, so I fortunately never had to deal with this nonsense. 
Maximum Damage
Not nearly as powerful as the Double Damage payload, this lackluster effect tends to make most players very sad...even if critical hits trigger more frequently. I am staunchly opposed to this payload. It's what I refer to as the "Bull Sh*t" effect. Here's why; Your weapon can do maximum damage all by itself. If it wants to do maximum damage, it will roll maximum damage on it's next damage roll. It doesn't need a critical hit for that. A critical hit means your attack does MORE than what is expected or normal. Silly, silly, silly game design right here folks.
Additional Attacks
Although I've never really used this method short of a few sessions in the long, long ago, I still think it's interesting. It allows players to make an additional attack every time a critical hit is triggered. Players could theoretically make attacks all day long with this method if they had really lucky attack rolls.
Fatality!
This one is extremely controversial for its seemingly "over-powered" nature. The target must make a DC 10 Constitution saving throw. If they fail, they are reduced to 0 hit points instantly. Otherwise, they take maximum damage. This method, if used properly, can create some extremely dramatic and memorable battles.
There you have it; The most popular, playable critical hit mechanics used in most D&D campaigns.
My Prescription
Ok, For those that skipped past everything just to see how this article ends, I give you this:
Realistic D&D: Method II with Fatality!
Gritty D&D: Method II with Double Damage
Awesome D&D: Method III with Fatality!
Snappy D&D: Method I with Additional Attacks
Classic D&D: Method I with Double Damage
Pharmaceutical D&D: Method I with Maximum Damage
Care Bear D&D: Method III with Maximum Damage
I like Awesome D&D, personally. Not sure about you guys...