I've been having a bit of a think about how I want to handle this one. There's not really any system I've played that I would describe as "surprising", so I thought about maybe taking a session that caused surprise.
I suppose for a surprising system I could consider Midnight, which was run several years ago and which caused a few issues because it feels like D&D except that in D&D you are the big hero and in Midnight you are low down and struggling to survive - and I (having played very little D&D-style games) got that straight away, but the others didn't and the game fell apart because I wanted to follow the plot of survival and they wanted to follow the derailment of all getting killed stupidly. Which was a shame, because I was enjoying the concept.Surprise! Playing the hero will get you killed in a world where the bad guys have won.
For an in-game surprise, it's going to take a lot to beat the look of surprise on the other players' faces when Svetlana and Noleski announced their engagement, but that was other players being surprised and really I'd like to talk about something that startled me.
And I think it may have to go back to something I talked about in last year's #RPGaDay - "Most Memorable Character Death" - where we ended the camoaign by accidentally ending the world... A WFRP's game run by Husbit (I've got a bit of a hankering for old WFRP's at the moment) in which we found a mysterious cult acting badly were aiming to rid the world of Chaos. Greater good and all that, we let them get on with their sacrifices. Sigmar was summoned and in turn summoned each Chaos god to fight and defeat them in turn. Course, turned out gods and mortal realms don't easily co-exist and the world crumbled around us. That was a bit of a surprise!