The first movie to ever blow me away was Star Wars (1977). I think I saw it 6 times in the theaters during the original release.
The next movie to capture my attention was Raiders of the Lost Ark (1981). This came out at a time when I was fascinated by anthropology and archaeology. This inspired me towards my first major when I got to college.
The next most influential movie for me was Jaws. I lived on the Florida coast when I was growing up, and it hit close to home. Not really a favorite, as it scared the mess out of me. But still, a very powerful film experience.
Honorable mention: Rocky and The Princess Bride.
I love movies - I even built a theater in my basement. I have a lot of recent movies that I have thoroughly enjoyed that have better acting, effects, cinematography, etc. However, nothing has influenced/inspired/amazed/entertained me like those movies from my youth.