Stealing - and reversing - Beedo's and the Hill Canton's idea shamelessly, here is another interesting topic. I'd love to see anyone else grab this and run with it too (and if you do, tell me and I'll link to it).
How do you build a better PC? What are three things you can do as a PC to make the game better?
What can you do as a PC to make the game better? Here are my three - although one has a sub-rule, which is kind of cheap, but I think they are related but both worthy of expansion.
1) Be Reasonable. Also known as "Don't be cheap" and "Don't be a munchkin." So, you have a sword out, shield on, and you are opening the door . . . while engaging in a Wait maneuver and fully prepared to defend against an attack from the front, sides, above, behind, and below. Oh, okay. You fell down the well while mapping, but the map isn't wet and none of your potions broke, but they are within a 1-second action's reach? Yeah . . .
If you act cheap, the GM is invited to cheap you back. Be reasonable. Picture the world and engage in it. Picture that door and think, damn, I need to put my sword away. And I guess I would set off a magical door handle trap because I'm grabbing the door.
GMs generally do not punish folks for demonstrating they are engaged in the world and acting according to what they see. You'll lose a paper man here or there doing this, but everyone will have more fun.
You have to talk to the tavern wench, trust the slimy thief (at least a little), buy a new hat, open the door.
Remember that ultimately the game is about role-playing, so you have to do it. Don't just sit there. Even in an old school "roll up a guy who dies 10 minutes later" game, get into it.
2) Ask questions that show your intentions. I mean ask for details or helpful hints, talk to NPCs, or generally "look around" in such a way that it makes it clear what you want to see. Open-ended questions with no goal tempt a No from a GM. GMs don't want to say no, but they sure as hell don't want to fall victim to "Can I do A?" Yes. "B?" Yes. "C?" Uh, I think so. "So I can do D, because it follows from A, B, and C, and D is a total game wrecker! Awesome, I do it immediately!" GMs get suspicious of open-ended questions asked with no reason in mind. We've all seen Colombo and we've all had players try to snake gunpowder, ninjas, and especially gunpowder-using ninjas with a series of leading questions.
Not only that, a good question that shows your intentions invites the GM to say yes, because you're adding to the world, not trying to fish for random information that may help later.
Here is a good question: "Is there alley I can duck into? I want to hide in the trash to elude the guys shadowing me."
Here is a bad question: "What do I see?"
Here is another: "Is there an alley?"
The good question is good because you're telling the GM what the consequences of saying yes to you are. You've put a specific cool scenario in the GM's head - "Wow, yeah, that would be cool if he ducks in the alley, hides in the trash, and then his shadows walk past him . . . " and the GM can run with that. You've asked for something specific and plausible. You didn't ask an open-ended question that actually shuts down possibilities. The bad questions do just that. "What do I see?" sounds fine until the GM doesn't mention an alley or a wagon full of hay or a fruit cart you can overturn. Then it's NOT THERE. It's too late to put it in when you say, "Oh, I was hoping to duck into an alley." Even, "Is there an alley?" is too open, because you've left your intentions too open. Why do you expect one, and if I say yes, what do you want with it?
Even a GM that says "No, sorry, no alley" knows you're looking for a place to hide, and might say ". . . but there is a wagon full of hay . . ." because he knows what you're shooting for.
This works with everything. "Do they have an armorer who could sell me a lycanthrope-killing weapon?" is better than "I go sword shopping. What do they have?" Odds are they don't have a lycanthrope-killing weapon, but they might have had you mentioned it. Or the armorer might know the mage in the tower at the edge of town has a henchman who used to hunt werewolves, and he needs some magical components fetched for him . . . and adventure ensues.
3) Respect the flow of game. What is more important - a smoothly running game session, or stopping the game for 15 minutes to check if you get a situational +1 to Stealth because of your boots on this surface? Let the details go, and let it slide, as long as play keeps rolling. Know what you want to do when you turn comes up, don't wait until it's your Speed or Initiative Number or Movement Phase to decide what to do - or worse, find out what's going on. Asking for a clarification is fine ("Which guy looks more damaged?" or "Was the guy with the broken axe on the left, or was it this guy on the right?") but not "So, where is everyone and what are they carrying?"
A related subrule of this is to Know and Own Your Character.
Know what your spells do, what your equipment does (and costs and weighs, and where it is), what damage your weapons do, and what your skills do. You really have one playing piece to track, so keep good track of it. Make it as easy for the GM to run a game for your character as possible. It sucks to GM for, and play next to, the guy who doesn't know which equipment sheet is current, how to roll damage, how to roll to hit, what his powers do, or how his spells work. Or even where his PC is. Keep track of all the stuff you can and know its specifics, and you'll greatly help your GM. This alone will ensure you get all those bonuses you are owed, that the GM will trust your assessment of your bonuses and penalties, and that the game will run smoothly on your turn. You don't need to be a rules expert, you just need to be a "my character" expert - know your own rolls even if you have no idea how those numbers were derived. Don't forget stuff like Durkon does. It really disrupts the flow of the game.