The official question - "Which RPG has the most jaw-dropping layout?" - felt too much like a combination of Day 12 and Day 19 for me to want to answer (also the hyperbole of the question made it difficult - I could talk about RPG's with layouts I like, but I don't feel qualified to judge which is the "most jaw-dropping"), so I went back to the alternative questions. The one I've gone with reminds me of Day 5 from the first year of RPGaDAY: "Most old school game owned", but my answer there - AD&D - isn't a game I've played, so I can talk about something else here.
I've had a think and done a bit of research, and it looks like it comes down to either Call of Cthulu and Warhammer Fantasy. It all rests on which edition of Call of Cthulu Husbit's brother ran: I know I've played both first and second edition WFRP. WFRP was first published in 1986, the same year CoC reached its third edition.
Call of Cthulu was run by Husbit's elder brother either one summer holiday while I was at uni or at some point in the couple of years after. It was a 1920's game, which suggests an earlier edition. I played a dilettante, Husbit and another playing were former army officers, and I don't remember the others. It was a bit of a strange game: Jules stuck to the rules of the book, which meant that someone ended up with a phobia of horses as a result of hearing a gunshot while we were on a boat. I found the system clunky and frustrating and I've never been a fan of Lovecraft. (I'd read M R James first and wasn't surprised to learn Lovecraft was a fan: his writing always struck me as a poor copy.) Overall, it's not one I'm in any rush to revisit, for all I've heard great things about friends' games. I just think there's better horror games out there.
Husbit was the first person to run WFRP for me, which I talked about a couple of times back in that first year. It was also the first RPG I was ever exposed to: some schoolfriends had got their hands on it and wanted to play, but none of them wanted to run it, so they asked me to read the rules and run for them. I dutifully borrowed the rulebook and set up an encounter involving finding some goblins in a cave... and then no one had time to play. I've still got the rulebook!
I've had a lot of fun playing WFRP, first and second edition. One of my biggest complaints with D&D-style games is the class and levelling restrictions, so I expected to have similar dislike of the career path, but I found I really enjoyed it - far more flexible and less punishing of multi-classing. It's a game I fully intend to play again - maybe even checking out the newer versions sometime.