If everyone is special, then really no one is.
The first thing to take into account in using 3d6 instead of 1d20 is the fact that you end up with a much more average roll. With 1d20 you have a 5% chance of rolling any number. This means that you are just as likely to roll an 18 as an 8. In game, this means that, barring bonuses, you are just as likely to shoot the bad guy in the head, as to shoot his goat.
With a 3d6 however you have a similar range of numbers, 3-18, as opposed to ,1-20, but you are much more likely to get the result of a 10. This is because there is only one combination of dice that gets 18, three 6’s. There are twenty-four combinations that get you 10. In game this means that spectacular success and failures happen fewer and farther between.
This makes the numbers on your character sheet matter more. If you are more likely to land a few points from 10 on a die roll, then you can't roll hoping to get that 17 so you'll succeed. Your bonuses will mean a lot more. And in an RPG your bonuses and your character sheet are you. So this means that your character is more important than the dice you roll. This character is good at basket weaving not just a PC on a lucky streak.
Tomarrow I'll go over what this does to combat.