I write and revise in order. My brain does not consider it optional. Save for going back to quickly make a note, add something in one particular place, or find a specific detail, I do everything in the order it happens in the manuscript (generally chronologically, as far as it goes). For the most part, it helps me keep everything straight, remember when twists are revealed, remember which information comes when, what certain things happen in the mc's emotional arc, etc. I think it's a pretty natural way to approach things. I mean, it is how I read, after all. ;)
It's not always a great approach to writing and revising, though. If I get stuck, I have a really hard time skipping over a scene and coming back to it later. So if I want to take a break from it and work on something else, I usually have to pick something outside of my manuscript. A totally different project. I can also usually work on the query or the synopsis, or outline something new, so it's not all bad, and I get other stuff done that might make my life easier later! But. We all know how frustrating a day or two (or, let's be honest, a week or two sometimes) away from the manuscript can feel. (That is, until you return to it refreshed and realize it was worth it.)
A dear friend and critique partner of mine does NOT write in order. (She'll know who she is when she reads this.) Quite the opposite: she sees scenes in her head and she writes them down, regardless of where they go in relationship to each other. And her brain has an uncanny knack for fitting them all together later. (Seriously. It's impressive. I could never make my brain do that for me.)
(I've tried it, too. The writing out of order thing. All I ended up with was a mess that didn't make sense, and I never did finish that novel. Didn't even get close. This is not a skill I possess.)
I'm guessing a lot of people are somewhere in between. Writing mostly in chronological order but having the freedom to jump around, or working off an outline so that you can write the "fun" scenes first and the connecting stuff later, or skipping over stuff with far less anxiety than it causes me if the need should arise, or starting with the scenes you see vividly, and then working from the beginning...I can think of a bunch of other examples but I'll stop now.
I am really curious, though, as to how everyone else works. How is it for you: order, random, or somewhere in the middle? If you want to go into detail, please do! I would very much love to hear it. :)