Gandalf falling was the first, even though I knew he'd return in the second movie. And yes, it wasn't so much his "death" as it was his friends' reactions.
I sympathized with Boromir because I completely understood what he was trying to do. He didn't want to destroy the ring when it could save his entire kingdom. He wanted to return triumphant, maybe with Aragorn as a brother. He didn't want to hurt Frodo, or anyone else for that matter. All he cared about was his people, and if he wanted to return gloriously, more power to him. I've never hated a character for wanting something for themselves, especially when "destroy the ring and everything will be better" is so incredibly vague. Sam, Gandalf, and Boromir were my favorite characters in Fellowship, and coincidentally, they're the ones who provoked the greatest emotional reaction.