Amazon recruiters approached me first on LinkedIn and invited to one of their off-site hiring events in Europe. I didn't feel like interviewing with them back then as I wasn't sure I could pass but still decided to try.
Communication with the recruitment team was surprisingly flawless - I didn't have any issues with timezones (I was based in Europe, they were from Seattle/Bay Area), there were some last-minute changes that didn't affect anything/caused any trouble. HR provided me with tips on how to pass the interview and shared some online/offline resources on how to get prepared - they also put a lot of stress on their company principles.
After the initial tech screening and a Skype call with one of the recruiters, I was invited to the hiring event. Amazon rented the whole floor on one of the top hotels in the city, all the candidates were assigned a room and the interviewers came to you - 3 interviews for algorithms/data structures, 1 for system design. The organization was really superb, interviewers were very positive and eager to share their experience.
In the end, I didn't get an offer, but I'd say I'd definitely try to interview with Amazon again.
PS. From what I read here, maybe I was just plain lucky to have a positive experience interviewing with them :-)