I would like to know, what was that one movie that you obsessed with when you were a little kid? We all had one. But what was yours:
For me I really enjoyed the 1997 Titanic movie. I was big into Titanic at the time and that just made me like it even more.
Star Wars. I was 7 when it came out. It pretty much was my reason for living for about 4 years.
Star Wars for me too. I was 12 when it came out and pretty much obsessed about it for a couple of years after that.
As a really little kid I was obsessed with Disney’s The Aristocats. I named all my stuffed cats after the characters, borrowed my parents’ jazz records, and set up little jam sessions with them (the cats, not my parents). I think I was the only kindergartner around who listened to jazz. 
Godspell.
Close Encounters of the Third Kind. With Star Trek the Motion Picture and Star Wars coming in 2nd and 3rd.
Another Star Wars here 
Since this topic is about movies, it’s better suited for Cafe Society. I’ll move it there.
Back to the Future and Goonies.
The Iron Mistress. Just the knife.
King Kong (the original). I watched every showing I could when it periodically came on Million Dollar Movie in the 1950s - every weeknight, and several times on Saturday.
Star Wars
also E.T. the Extra Terrestrial
Well, this is somewhat embarrassing, but it was Disney’s The Black Hole. Which is an utter piece of shite, and even my thirteen-year-old self should have known better. Somehow I missed Star Wars completely (I didn’t see any of the original trilogy until they became available on VHS); I guess I just wasn’t into SF at the time. But I remember reading about The Black Hole and begging my parents to take me to see it, and my father reluctantly did. On the upside, it did coincide with that period of my early teens when I was becoming voracious about reading SF/F, so it at least fueled those fires.
I define obsessed a bit differently than others,I think. To me, it means the movies where I went through an extended phase of watching the video tape over and over and over, but not really related to going to see them in the theatre. I can think of three:
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Sleeping Beauty (I was obsessed with Maleficent)
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Michael Jackson’s Moonwalker (holy fucking shit I was in love with Michael Jackson as a little kid and I loved this movie, even though it made no sense).
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Willy Wonka and the Chocolate Factory (I love love loved Gene Wilder’s Wonka; set me up for a lifetime of Wilder fandom).
And I’ll still watch any of them excitedly to this day.
It’s funny–I absolutely adored this movie, and I’m pretty sure Wilder’s Wonka was my first love ever. I think he had a strong effect on my preference for smart, sarcastic guys to this day.
I didn’t grow completely obsessed with the movie until many years later, though, because I saw it once in the theater when it first came out, missed the end because the kid with us had a meltdown and my mom made us leave, and never saw it again on TV until a long time later. That’s why I didn’t include it on my list here, even though it’s had a huge impact on me throughout my life.
Two movies come to mind, both within 12 months:
The Longest Day (1962) came out the summer I turned 13. I saw it four times, and thought it was the best thing going. I probably watched it again much later when it showed on TV, but by then it had lost some of its punch for me.
Lord of the Flies (1963) came out the following spring, I believe. I only watched it once, but it had a profoundly depressing impact on my outlook for quite a while. I still can’t bear to watch it.
Manitou, 1978.
I saw a number of films in the 70’s that had a huge impact on my future self, including Star Wars, Deadly Flying Guillotines, etc. However, looking back, nothing affected me more than Manitou. I saw it in the theaters with my family when I was about 4 years old. I had nightmares for months afterwards. As I got older, I realized I would never, ever get scared like that again, and that made me sad. Every movie I see now, I’m hoping it will thrill me like the 4 year old that got scared to death watching Manitou.
Probably E.T. I thought the bicycle riding through the construction site near the end was the coolest.
The Sound of Music. I used to have dreams about the gazebo and the marionettes. I can still sing the entire score.
I think I first went to see it when it came out or shortly thereafter, so I would have been six or seven years old. (I had very permissive parents, plus we were living in either Greece or Turkey at the time - Zorba is set in Greece.) I’ve probably watched it at least a dozen times since then, plus read the book. The part I recall striking me as a kid was Zorba’s speech about it being OK to be crazy, and his dance with the Alan Bates character on the beach.
I also saw Lord of the Flies as a kid and agree with Roderick Femm - a disturbing movie, especially from a child’s POV.
On a lighter note, I saw Disney’s Fantasia as often as I could; it was a frequent matinee at the US military base near where we lived. I still think that’s an amazing film, especially considering it was made in 1940. It instilled in me a life-long appreciation of classical music, too.
Grease.
We had sock hops before school on Fridays. After I saw it for the first time, I begged my mother to take me to the local thrift shop to mine for penny loafers, hoop skirts and anything else that couldn’t won me a Pink Ladies’ jacket. I’d listen to my dad’s old records like “It’s my Party and I’ll Cry if I Want to” and pretend I was Rizzo. We never hardly ever went to the show, but I was allowed to catch it at the dollar movie at least once a week for probably a year. Before I even realized it, I’d already seen it 28 times. I could tell you all the lines by heart and I tried to make all my friends recreate the dances. I even watched “Grease Day USA” on TV. It was totally epic in my world.