I agree with Greiger, crits have had a lot of thought put into them, the only time TF2 shouldn't have them is during professional tournaments when random chance cant be a deciding factor. Unfortunately people remember the times they die to crits not the times a crit helped them take out half the enemy team or gain a revenge kill on that enemy that has dominated them the past 2 games.
I dispute this notion, especially when the random chance is skill-weighted and contests are frequent enough that the luck won't decide all by itself the outcome of a statistically relevant number of encounters. In other words, since you get so many chances to kill your opponents and go for the objective, it's not necessary that every single encounter be 100% determined by player skill. It's acceptable to have some element of chance as long as the system is both favorable a more skilled player and mitigatable by the unfavored player through skill. Getting more crits as you do more damage definitely counts for being skill favored.
That's not to say that I think TF2's crits are 100% appropriate for tournaments, though. Specifically, very close range crockets are impossibly hard to dodge and spell certain death for 8 of the classes and near-death for the Heavy. Crickies are also stupidly deadly, and most other crits (except shotgun crits) are far too deadly and hard to avoid to be called mitigatable. In more cases, getting hit by a crit means you die, and if you're not dead, you're very close. But the point I'm trying to make is, deterministic winner-favouring non-dominating random chance is not something to automatically shun in tournaments. Look at Poker. People bet hundreds of thousands of dollars at tounraments on a game where winning or losing a hand is determined by chance alone, yet you can't look me and say with a straight face the Poker isn't a skill-intensive game. (Before anybody PM's me, all I'm saying is that no matter how you bet, despite the fact you'll lose a ton of cash, you'll still win a couple hands.)
You have to look at luck elements on a case-by-case basis. Sometimes, the random chance adds something to the game. Specifically, if a skilled player can overcome the advantage the dice have given their less skilled opponent, then you're really only changing the path to victory, not the fact you actually won. A highly varied number of situations for the player to overcome is indicative of a fun and highly skill-intensive game.
So I think the crits system could be improved in many ways. The most important one boils down to changing it so you have a 7% to 10% chance of a mini-crit, but as you do more damage, more and more of those mini-crits get turned into full crits. That way, skilled lucky players get rewarded with cool kill-streaks while less skilled players still get chances to take down more skilled players, just not in an "I crit, you die" kind of way, it's more of an "I mini-crit, making up for the attacks I missed with earlier" deal.