In comments below, Pedro Beltrao of Public Ramblings says:

What I disagree with is that we should go ahead and try to change things starting with the assumption of good faith. There is a percentage of people with bad intentions, this is clear, so we should plan for this. Open systems like wikipedia and digg are having problems and are taking steps to solve them. I suggest we keep an eye on these pioneering online social systems and see what solutions they come up with.

He’s right, and it’s an important point. When I said we should assume good faith, I wasn’t clear. I didn’t mean we should naively pretend there are no assholes in science. What I meant to convey was that, in addition to the sorts of measures we can learn from systems like wikipedia, we should do two things: 1, change the emphasis of the culture of science from suspicion to trust; and 2, have more faith in our ability to identify and deal with cases of bad faith as they arise. In other words, relax.
I think that we have good reason to approach fellow researchers as potential collaborators rather than potential scoopers (see below), and that when bad actors try to take advantage of that approach we also have, as a community and as individuals, the means to deal with them. When I say “the means to deal with them”, I mean to include the sorts of checks and balances that Pedro is talking about.
Plentiful though they are, stories of scooping and other assholery are vastly outnumbered by the stories you don’t hear, precisely because they are the stuff of every day:

• the PI who lent you her unsubmitted grant so you could copy the format for your own
• the postdoc who spent half a day digging through the -80 freezer to find the plasmid you wanted
• the NIH staff scientist who sent you transgenic fibroblasts in response to an out-of-the-blue email
• the paper you’re an author on even though all you did was teach someone a technique they didn’t end up needing¹ (“we said you’d be an author, so you’re an author”)

and so on and on. Those are all true examples from my own experience, and I’d like to invite readers to add their own in comments. It would be nice to hear about the up side of the scientific community for a change.

¹ I should clarify: an acknowledgement “for technical assistance” would have been more appropriate, and these days I would insist on that. At the time, I gave in and took the free ride. Mea culpa. I included the example just to point out that researchers are often generous even with that most precious commodity, publication credit.