In the UK, I think there is a paper application stage to go through first?
Then on the first day of auditions, where you see the thousands, there are 2 producer auditions. Then there are callbacks, auditions for Executive Producers and then the judges.
With 182,000 applicants to X Factor this year, if each took 3 minutes to audition and the judges worked 9am-6pm with a one hour break for 5 days a week, it would have taken 227 weeks to complete the auditions. So if they started for XF5 in May 2008, they could finish in September 2012 and the show would have to become a five yearly event. (About 4 years and 4 months.)
So a selection is taken to represent the auditions process on TV:
The very good
The decent singers with a good story
The very bad