As a GM, I firmly believe that one of the key jobs you have is to make sure that each player has a moment of cool that they can call their own. Something that stands out as a "that's why this person is awesome" or something that can be pointed back to weeks or months later as a "that was totally radical!" However, it's not always as easy to get one for every character.
What is a 'Moment of Cool'?
There are several definitions for this floating around out there, and odds are that if you ask your players you may get a few more. One of my players defined it fairly well as "something I've done that people talk about out of the game as being cool." I've personally defined it as a spotlight moment, or a moment when all eyes are on that one character in the game. The point is, depending on our group you will get different variations, but in almost all cases it is something big that the character did that was either incredibly useful/damaging, or incredibly memorable in some other way.
Making It Happen
So how do you make them happen? Well, in honesty you can only do the first part of it. You, as the GM, can present the situation and the opportunity for it. It is then up to the player to play into that moment. For example, you could set it up for someone big and nasty to have a one on one fight with one of the fighters in the group. Or for a character to make a big decision that shapes the effect of the story.
Sometimes, the game itself will present these naturally. A grenade will fall into the group, and a character will try and dive onto it. The biggest point here though is that all you have control over is the set up. After which, the player must play into it. Because of this, especially if you are trying to give one specific person their chance to shine, you may need to talk to your players that the opportunities are out there for the taking.
One of the dangers with these moments is that some PCs are by their very nature glory seekers. These are usually played by the players who know the rules, or your GMing style, and they aren't afraid to play by the motto "go big or go home." Generally, these people can be great to have in your game, because they will show the other players what is possible. However, you may have to jerk their leash a little when trying to give someone else their special opportunity to be awesome. It does no good to give Bruno the Rogue his chance to be a Batman-esque bad ass against the Dark Knight Triptomere if you put Paladin Ragnar and his epic smite of awesome in the same room. Why? Because Ragnar is going to bash the shit out of Triptomere and bring the fight to a level where Bruno can't do his stuff.
Because of this, you may want to separate people out for certain chances, or just not be afraid to cheat a bit to give one person the nod. If you do cheat (and I don't recommend it as anything but a last resort) make sure that the PCs don't know that you are. Nothing ruins a moment of cool faster than knowing it is a scripted event.
One Man's Treasure...
The other thing to be careful with is the fact that the very act of being awesome often means someone else has to be lackluster. For example, it is totally bad ass when Ragnar beats Triptomere in a fight after Triptomere just handed half the party their asses. Especially if Ragnar does it with awesome rolls and other things. However, by the very fact of that it means that half the party just got their ass whooped by one person...and then he was taken out by just one player. Yes it is awesome, but if that sort of thing keeps happening, the other players in the group might feel resentful. Or worse, they may feel that their character exists to make others feel awesome.
Spread It Out
Enough with the bad. Let's talk about the doing. When you go to give the moments of awesome to someone, make sure to be ready to give them to others as well. They don't have to be in the same session, but have things prepared for each character to have their cool thing they do. Maybe not all of them are "talk about outside of the game" big, but you want to give everyone their time in the spotlight and challenges that their character is ideally suited to be the one to help overcome. Which brings me to my second point.
Focus The Challenge
If someone is built for one on one fighting, then odds are their moment of cool will come from a one on one fight. The same with a character set up for group fights, or a hacker with a hacking problem. The point? Try to focus the problem to the character who you want to look cool. It makes it a bit more obvious that the challenge is for one person in particular. In a group situation, you can spread out the moments easily just by doing this. For example, the melee specialist gets their duel, while the group specialist holds off the hordes of zombies, the demo expert sets up everything to go boom, and the vehicle expert has things ready to race off quickly. Everyone gets their chance to shine, everyone is happy.
Alternatively, a character's moment of cool can come when they are challenged in an area that they're not strong in. The social butterfly suddenly has to survive a firefight, and does it. The problem here is that you will probably need to split the group in order to do this. After all, how are you supposed to shine somewhere you're weak when the person who is strong in it is right there? Still, sometimes these can make for the most powerful moments in a story or game, if you do it right.
Play It Up
The most important thing to remember though is this. No matter how it goes, play up the moment of cool. If you act like something is ho-hum or expected, than the players will too. If you act like it is a big deal, and play it up in game as a big deal, than it will be remembered as a big deal by the players. Even something as mundane as making a skill roll to fix a jeep can seem more awesome if it is played into properly. If you remember nothing else, remember this. When it happens, before it happens, and after it happens: Play. It. Up.