If its something that I care about watching, which is most of what I'm watching otherwise i wouldn't waste my time, then yeh, I do care about spoilers. I'm there purely as a viewer, so I'm there for the whole ride. Knowing the plot of a movie or TV show or knowing who is going to turn evil or who is gonna die just gives me less of a reason to watch it. That's why I rarely follow rumors for Tokusatsu shows outside of who the next Sentai/Kamen Rider/Ultraman is and what the general plot will be. Other than that, who the next rider will be, what's the next power up, who the final bad guy will be, are things I'd rather find out as the show goes on. It's part of the fun for me, its why I watch the show.
It's a constant struggle between me and Aoi Kurenai. He loves finding out the latest news on shows, episode summaries, plot twists, etc. And I constantly tell him not to tell me anything because I wanna find out on my own. Like, for Fourze, a lot of clues are in the names of the characters, just jumbled around to make it a tad less obvious. I guess if you're japanese, you'll probably get it right away. but I wont, so I try my best not to look for what they mean. And for shows like Fourze, which I'm very lukewarm about, the less I know, the better cuz the mystery of the story is one of the few things keeping me from dropping the show.
So in short, yes, I do mind spoilers and try my best to avoid them when I can.