When people talk about the difference between games and stories, one of the most important points of distinction takes the form of the characters. When you create a character for a game, you are focusing primarily on capabilities, those things the character can do. When challenges come up in play, tension is created by raising the question of whether or not those capabilities, modified by a randomizer and optimized by player choices. That uncertainty means every part (especially capability and choice) is meaningful. A talented GM or well-designed scenario will put the whole event in context, giving it some meaning and resonance, but that's not a necessary step. Things work (in a well designed game) without it.
On the other hand, when an author creates a character for a story, he has entirely different considerations. The capabilities of the character are never in question, and when faced with a challenge, he will overcome it or not as based on the author's needs. But at the same time, the author must provide context, because that is what matters to telling a good story. That is to say, the author does not care if the character can climb that wall, he cares about why it matters whether or not he climbs that wall.
These are very different goals, and at their core, they're contradictory ones, but that doesn't mean that there's not room for stealing between them. The more a player likes context for his actions, the more he might want to look at the things that make a good character in fiction (Connections, motivations and so on), and a fiction author would be well served to construct characters with their capabilities in mind so it doesn't look like they're cheating when the character proves capable of something.
But there is an interesting point of overlap between the two in that both depend on convincing challenges - that is to say, challenges where the outcome is in doubt. Even if the author and the game master have different means of resolution, both are poorly served when the player/reader looks at a situation that should be important and feels there's only one way it could possibly play out (unless someone cheats).
The most obvious place this comes up is in capability-centric fiction, which a lot of adventure fiction is, most notably comic books. I talked a little bit about Batman last week, but let's flip the camera and talk about Superman. Superman is a tough character to handle because he is so capable that it's difficult to convincingly challenge him. Because he's so powerful, just throwing more powerful guys at him is a poor solution, because they have to come from somewhere and because too many such guys and Superman's role in the setting starts getting called into question.
This puts the author and the GM in the curiously difficult position of needing to really work to find a good challenge for the character, and they likely turn to the same place - challenges that strike at the place where his power is not going to be quite so overwhelming. Hit his friends and family, bring in tough moral choices and generally proceed from the assumption that yes, he's crazily capable, so we'll work with that.
Now, this is where we start getting the weird divide between gaming and writing. For a writer, we're doing ok, albeit working very hard to stay fresh and interesting since we're trodding over ground that has been trod many times before. There's a temptation to change things up by perhaps introducing a new weakness or a change to capabilities that gives him new material to work with. In contrast, in gaming, Superman's player's been stockpiling his XP so that he can buy off those annoying "Weakness: Kryptonite" and "Dependant: Lois Lane" disadvantages so that his character will eventually be perfect.
And that, right there, might be a problem. Proceeding from the assumption that playing the game is fun, Superman's player's goal is to be so successful that he will never be challenged, which means he'll have nothing to play, which means...no fun.
It's an extreme example, but a lot of people play with that underling perspective. In attempting to address their own flaws or weaknesses, they forget that the purpose of the game is to provide challenges for the player and that even if you resolve one set of challenges, there are always others. And this is where there's a little something to be learned from the author. See, the author knows that things need to be kept interesting, and the first place he'll look for interesting things is the character. He see's Superman and see's things like Kryptonite and Lois Lane and he views them as opportunities to tell a story, not as things that weaken the character. That's a useful perspective for a gamer too.
See, when you take drawbacks (whether they're mechanical, or just something you write into the character), you are steering the game. Provided you have a GM who takes any authorship of her games then you are telling her about the kind of problems you want to have. And since you're going to have problems anyway, wouldn't you rather like to have some say in what they are?
The bottom line is that you do not need to be "creating a story" or taking an author role to appreciate that your characters problems and limitations can be as essential to your fun as their capabilities. Even if you never care about the context of the challenges you face, and the story elements implicit in that, it's a simple matter of combinative math. The problems you bring along with you will make the challenges you face more interesting and personalized, and that personalization also means you'll have had time to think about solutions. Which means you're more prepared, and who wouldn't want that?
1 - In most games. There are, of course, exceptions.
2 - If taken into play, the logical extension of this idea is to have character success or failure depend upon "the needs of the story". This is one of those ideas that people suspect story-driven gamers are proposing, but I don't think anyone is actually a big proponent of it. If that's really how you want to resolve things, there's a reasonable question as to why you're playing a game.
3 - If you ever want to see how much meaning can be squeezed into the simple act of climbing over a wall, then pick up Lois McMaster Bujold's "The Warrior's Apprentice" and read the first chapter.
4 - That is to say, an author can decide his character can fly a helicopter at the moment it comes up, but the character will be more consistent if that fact exists on his "sheet" from the getgo, so it doesn't come out of left field.
5 - If the protagonists main assets are his gadgets or martial arts skill, then capability is a big part of the fiction.
6 - You might not. You might have a GM who uses only published adventures, though realistically that's only on option for D&D and is variants, which don't offer much mechanical support for drawbacks anyway. If that's the case, then keep your head down, bring a 10 foot pole and keep checking for traps. I mean, yes, you can try to convince the GM to use your personal enemies rather than the generic ones from the adventure, but let's be frank - if she's only using published adventures to be begin with, then she may not be comfortable with changing things up like that.