Note that I tend to take a very methodical approach to writing, and that I tend to think of my individual threads as but pieces in a much larger legendarium.

1) How do you define plot?

At its simplest level, I define plot as an interconnected hierarchy / series of conflicts and resolutions, that together tell a story. One step in a plot takes a given set of settings and characters and transforms it into something different, with new sources of conflict and possible resolutions. The plot as a whole takes a starting set of settings and characters on a journey until a convenient ending point.

2) How do you develop plots in your own stories?

I tend to develop plots on three interconnected levels. The first is on the story level - what is the conflict in this setting, and what roles do my characters play in resolving it? The second is on the character level - what development are my characters gaining from this particular story? What is the conflict that they're dealing with, how are they going to resolve it, how are they going to change as a person afterwards, and what effect is it going to have on their relationships with other characters? And finally, I think on a meta level - how does this story fit into my world as a whole? How does it resolve previous conflicts? How is it going to affect future storylines?

Based on these three levels, I identify key events within the thread. I can then start spotting locations, supporting characters, foreshadowing, sub-conflicts, etc., weaving them together so that they follow the logic of the world and the story that I want to tell.

3) What are the pros and cons you see in plotting (coming up with your storyline before writing your first post) and "pantsing" (writing the story and seeing where it goes)?

As my personal goal is to weave everything I write into a coherent and epic overarching narrative, I've rarely if ever "pantsed" before. I've never considered rigidity an issue, because it's a natural part of my workflow to work from the "must" events downwards. If I want to rewrite a minor event, that's easy enough; if I for some reason decide that one of these "must" events doesn't work, then it's worth taking the time to rethink that thread in detail. Working this way allows me to eliminate as many inconsistencies and plot errors as possible before I start writing.

Like Storm, though, I plan a lot less when I write with a partner because I don't know their characters as well as I know mine, and some people just aren't comfortable with the amount of preparation that I'm prepared to put into a story (I don't blame them!).

It's possible that "pantsing" a thread might allow you to come up with off-the-cuff inspiration that you otherwise might not have. I generally find, though, that planning out a thread in advance actually gives you more opportunity for such inspiration because you're spending just that much more time thinking about the conflicts, the characters, the setting, the resolutions. I agree with Kryos that it might work with the right group of people, and with others that it might be more fun if you don't have a defined outcome in mind. Unfortunately or not, that's never been the case with my threads.