Oh gawd, there are so many, and a whole lot of them have already been mentioned, so I'll just go with two that haven't come up yet.
One that always sets my spine tingling and which I've not seen on this list, is the moment in the first Jurassic Park where they're in the jeep, coming over the hill and it's the first time Alan and Ellie see the dinosaurs. The score soars into that classic Jurassic Park theme, and we the audience are swept up in their amazement. (Plus I was still young(ish) when I first saw it, and I hadn't yet been spoiled with millions of CGI dinos and monsters, so it was rather impressive to me too!)
A really, REALLY cheesy one for me is the ending of Austenland. It's not the best film in the world, but I love it! At the end, Jane's got home to her apartment and is taking all her Mr Darcy things down, her lifelong obsession finally burst. The saddest, most beautiful song is playing (Emmy the Great - Comic Books, check it out on youtube) and she's trying to figure out who the hell she is now. There's a knock at the door and she thinks it's her friend come round to welcome her back so she yells for her to let herself in. Turns out it's the dishy Brit she thought she liked back in Austenland (a big Austen-themed roleplay type holiday - details so not important!). He's come after her, and gives her back the book she left behind. The bit that takes my breath away each time is when she says 'you could have mailed it' and he's all taken aback, and has this momentary realisation that actually she might not be into him. It's so humble, and so much the opposite of the arrogant, self-confident leading man, and I just find it so endearing that he's done this big overblown gesture and for a brief moment is just massively deflated as he realises that he doesn't automatically get the girl just because he's there. He does, obviously, get the girl in the end, but that moment of doubt is just so real and so beautiful in a film filled with cheesiness and over-acting and lots of self-mockery.