Star Wars had a profound effect on my life in terms of shaping what I found enjoyable and setting a high-water mark for entertainment. Plus I used to watch it on Sunday mornings (when the "fake preacher" shows were on, as I called them), pretty much every week from the time I was 6 til I was about 12. So, basically, instead of going to church, I went to Star Wars. In the same way that years later you can hear part of a hymn or whatever and hum along to it involuntarily, I can hear part of a line from the film and finish it or even sound effects like R2's bleeps and boops.
Roxanne was a film that, as a kid, spoke to me. Steve Martin's character is awesome in that film. He's athletic, erudite, witty, irreverent, charming, and romantic, but he's also kind of overlooked. Particularly after I'd just started noticing girls, I identified with that. There's a part of me that still identifies with that, even though I'm a hell of a lot more confident nowadays.
At another point in time (late teens), particularly when I was feeling frustrated with life, Taxi Driver spoke to me. I certainly didn't feel like trying to shoot the president to impress Jodie Foster, but I sort of got the notion of not being able to connect on a level, and feeling isolated. I still find Late for the Sky to be this incredibly haunting tune, although it's taken on different meanings for me in later years. Oddly, I interpreted the ending WAY differently than most people do, viewing it as this culmination of a tale where a directionless, marginalized guy ultimately finds purpose and his place in the world. Oops... I see it differently now, but I still kinda like that interpretation better, even if I don't believe in it anymore.
L.A. Confidential convinced me that the Oscars are not worth watching and are a bunch of crap anyway.
Dune (the 1984 Lynch version) encouraged me to pick up the book, which would later lead me to reading the next three entries. God Emperor of Dune fundamentally shifted my view of humanity and the course of human history in a way that still resonates today, and it all goes back to watching David Lynch's trippy film.
Outside of that, I wouldn't say too many movies end up having a profound impact on me. I enjoy them, but they don't "impact" me or "speak" to me very often.