The longest app I can think of was for a Palladium system game (may have been RIFTs, might have been Palladium Fantasy, can’t completely remember) that wanted all manner of hoops jumped through. This may not be 100% accurate to the reality of the game, but if anyone remembers it from this process, chime in:
The application text required the following:
Full Name
Age at the time you entered play (had to be at least 19)
Full & Short Descriptions
Full Typed Out Character Sheet (IN THE PALLADIUM SYSTEM) including full inventory and the stats for any vehicles / power armor / giant robots you owned.
Full prose background, with one paragraph dedicated to each of the following:
Your character’s life from birth to 18.
Each year after 18.
Your characters history within the realm of any faction they may have been a member of.
Reason your character came to the region described by the grid.
Relationship history of your PC and any PCs you knew prior to coming to the grid area.
Rough ideas on what your character’s IC goals might be.
Then after typing out all of that mess, you got to sit with the staffer assigned your application and chat about anything they found peculiar for at least an hour as I recall, more if you were trying to be something on the far side of balance. (So for RIFTs, something like an Auto-G or Mega Juicer).
After that, you went into the approval queue. In an effort to have some sort of arbitrary control over the population of the game, the staff would take any approved characters and put them into a queue, and then at certain points each month, they’d let a few people finally go IC.