Had a 30 minute screening interview at a military-focused career fair - asked a few behavioral questions plus a fairly easy math problem. Got invited to an onsite interview - very professional impression; booked me a flight, car, hotel. At the Amazon site, eight of us cycled between four interviewers - a local, an HR person (also a local), a Sr. Ops manager, and another senior operations person who evaluated another math problem. Took about four hours. They each had a laptop with behavioral questions that apparently are designed to determine if you have demonstrated their desired behaviors. I got the "we're not moving forward" call a week later (good on them for making the decision so quickly). My best guess is I killed my chances with my answer to the question about my weakness (they call it "opportunity"). My answer, impatience, caused some concern about how I'd deal with people working for me. Lesson learned - follow the conventional wisdom to provide an absolutely innocuous weakness that would have little impact on the role.
Overall, my experience was positive - the recruiters did a very nice job maintaining contact during the process and actually responded to emails. Letting me know their decision in a week, though disappointing, proves it can be done!