The root of all fear
Not all fears are created equal. Your brave Norn in Guild Wars 2 might have a fear of dying anonymously and a fear of the undead, and the two are going to manifest differently. He won't flee in terror at the hint that he might die without being remembered, but he'll take steps to prevent it and it'll stick in his mind when it almost happens.
Every human being has fears, and while not every character you play will be human in the strictest sense, most have thought patterns close enough to human beings for the statement to still work. You need to know what those fears are.
Sometimes these fears do make a certain amount of sense. If your character watched wolves devour her parents, she's probably going to be uncomfortable around canids. Other fears don't make any sense; your character has never had a bad experience with dogs, but she's still just as scared of them. It's important to avoid the trap of letting every fear be a puzzle to be solved or a result of some deep-seated trauma. Sometimes you're just afraid of bees.
Equally important is knowing that not all fears are at the same level. In real life, I am scared of spiders, but that means I kill the damn things if they're in the house. I've known people who are scared of them and still catch and release the eight-legged bastards, and I've known others who freak out so completely that they can't even kill the offending arachnid. Being scared can produce a variety of different behaviors.
There are also some things that we're all scared of. No matter how nihilistic you get, most people are innately afraid of death. If you want a character to be scared without a specific fear, there are plenty of reasons for it.
Immersed in the terror
It starts at the back of your neck, that creepy tingling as your body goes into overdrive. Your eyes widen, your muscles start to tense, and you become quieter as you try to listen for sounds. Fear is, at its heart, a very basic survival instinct designed to make us get away from things that are going to kill us.
If you're unsure how to portray fear in the midst of an all-consuming terror, there's the key. Every movement of your character is focused on getting away from imminent danger. The entire fight-or-flight response is your most basic brain functions asking whether it's easier to kill or avoid the danger in question, at which point the intersection between instinctive responses and higher-order brain functions become really interesting to watch.
When your character is scared, is he one of the people throwing everyone out of the way while he runs? Or is he standing at the front telling everyone else to run while he holds off the seriously huge spider in the bathroom? Both make certain amounts of sense, even if in both cases the spider isn't actually going to hurt anyone in the first place.
Fear thrives on anticipation. It's why so many horror films love slow pans, creeping down hallways, and the like. The viewer (and sometimes the characters) know there's something down the end of the hall, but you have to keep waiting for it, picking along inch by inch, so that when it finally emerges, it's almost a relief to be thrown into a blinding panic.
So don't have your generally brave character rush headlong into the hordes of the undead. Have him pick his way along, knowing full well what's waiting but not wanting to face it. And when he's finally faced with it, seeing it shamble along, go ahead and have him run away while possibly weeping.
Or just have him be very uncomfortable about it until he can talk about it with someone -- that works too.
The only thing we have to fear...
Rolling characters with understandable fears is a good thing, but it also does raise an issue or two -- namely, that no one really wants roleplaying to turn into a game-specific equivalent of Scooby Doo.
The distinction between brave and cowardly characters is totally worth exploring, but it's an unstated expectation that your character is brave enough to not flee in terror every few moments. Being afraid of dying at the hands of some clawed lizard-thing is a very understandable fear, but it's why most of the people within the setting don't take a job that requires constant exposure to clawed lizard-things.
Give your characters fears, but don't make them slaves to that fear. Otherwise you wind up with characters who exist solely to complain about being scared, and that's not fun for anyone. (Unless you find that fun, I guess.)
Feedback is welcome in the comments or via mail to firstname.lastname@example.org. Next week, I'm going to tell you the sort of character you can play next, and because I'm generous, I'll give you a few choices. The week after that, it's time to explore the masquerade.
Every Friday, Eliot Lefebvre fills a column up with excellent advice on investing money, writing award-winning novels, and being elected to public office. Then he removes all of that, and you're left with Storyboard, which focuses on roleplaying in MMOs. It won't help you get elected, but it will help you pretend you did. If you need a refresher, check out the Storyboard Library.