Another tricky one, for me. I feel like there's two ways to answer this: by considering a game system, or a game session.
For the first... My first gaming group were pretty scathing of D&D. The Shadowrun's GM was particularly disapproving of how powerful you could end up, so I was surprised by how powerful it was possible to end up in Shadowrun! They also didn't like that you could reach a point where a headshot wouldn't just kill you, which seemed unrealistic to them (though that could happen in Shadowrun, too, and actually in real life). When I finally started playing D&D systems, I discovered a lot of what I'd been told wasn't strictly true (at least not in the versions I've played), though have to agree with the general feeling that alignment is more trouble than it's worth, being too subjective and leading to too many arguments. So I was surprised to enjoy D&D more than I expected - to begin with. Coming from a Shadowrun/World of Darkness background, I found the levelling and classes system to be too restrictive. I think it's why I usually gravitate to playing rogues: they're the class that's offered me the most flexibility. You can be a thief, a diplomat, an assassin, a sniper, an academic, a general do-gooder... And then the combat! It's so slow, and only having a single d20 means that 5% of the time you are guaranteed to fail badly, no matter how good you are. We went back for a one-off Pathfinder session after having played Savage Worlds Deadlands for long enough that we were all taken by surprise at how clunky the combat was, and how drastically it slowed the game, making it harder to enjoy the plot (until the GM made the last few combats more cinematic than rolled).
So D&D surprised me by both being less bad than I expected, and also worse.
For the second, I'm struggling to choose. Campaigns often end up in unexpected places: when we started Pathfinder, I had no expectation of ending up married to the King; when I played a game based on Final Fantasy X as a White Mage from Besaid, I had no idea I'd end up a Summoner. But these are things that grew out of play, so it's not exactly fair to call them surprises. For that, I think I need to look at individual sessions, rather than the campaign as a whole.
Vienna exploding around us in Aberrant was certainly a surprise. When you're a superhero, you often think you can't fail, which Adam felt like he had for a long time after (Chrissie, more practical, tried to reassure him it wasn't his fault, but his ego never quite believed her). There's been a lot of twists and turns in Exalted, too, but I keep talking about Exalted at the moment, so I'll leave those for today (also, most of them haven't been written up yet). Tark's death was a horrid surprise that really got under my skin - I think it was the first time I really, truly felt with my character, which was horrid and thrilling and exciting.
I don't know. I don't feel like I have a good answer to this one. Looking forward to seeing yours - don't forget to add a link in the comments :-D