Do any experienced DMs not have house rules for critical hits? Unless you're playing something like DCC, with a deep and robust crit system, I think it's a must.
Here's how I handle them in my Labyrinth Lord campaign. On a natural 20, the number of damage dice is doubled (so a sword that normally does 1d8 damage does 2d8 on a natural 20: note that bonuses from strength/magic are not doubled). The player rolls a second d20 on my homebrew table to determine location. Each location has some special effects, such as further penalties which will persist until the critical hit is healed. Most locations can be severed and some can cause instant death. In these cases, the attacking player rolls d100. If the result is equal to or under the total amount of damage inflicted by the hit, sever or death results.
*Full disclosure: as I’ve gotten older and my taste in play has grown steadily simpler, I’ve used less and less of the options on this table. Nowadays? We just roll the 20 to find location & make the % check for sever/death. I kill enough characters without adding hit penalties from a crit to the thumb. That being said, I’ve had a blast in the past with these extra flavorful crit results. It’s up to you what you use- never a wrong way to play.
I’ve modified this table from one my high school GM created. It's evolved quite a bit over the years, but I still keep his name on it in honor of George’s original creation. I present to you, the Wakulik Critical Hit Table.