Beginning: Raising Arizona - I think that it was something like 10 minutes before the opening credits, simply awesome.
Ending: The Road Warrior
Ahhhh, beat me to it.
One of the best beginings is The Player.
Beginning: Star Wars, definitely. First, the receding prologue. Then, quiet tinkly space music, as the camera drops to show a dusty-looking planet with two moons. The music picks up JUST a little, and this big spaceship enters from the top of the screen and passes through. Then, just after the big spaceship’s engines pass the middle of the screen, the music gets dark and ominous…and an absolutely enormous spaceship comes into view at the top. And passes through…and passes…and passes…and passes…and passes…
To put it in the current idiom, it’s just, like, WHOA!
You had to see this at the theater when it was first released to understand what a stunning, game-changing moment this was. You just didn’t see that sort of thing, ever, let alone at the beginning of a movie. If you ever expected to see something like that, it was at a climactic moment, not to OPEN a movie. You knew you were in for something different from the get-go.
I saw it on a GIGANTIC screen, and yes, as a 12-year-old, it was WONDERFUL. 
Start-Sling Blade
End-The Good,the Bad and the Ugly
Start: the whole opening sequence–which ends with a car crash–and then the apocalyptic opening credits (with Johnny Cash singing “When the man comes around”) of the newer version of Dawn of the Dead.
Beginning
The Matrix: Trinity almost gets caught.
Ending
Rocky 2: “Yo, Adrian! I did it!”
Princess Bride: Literally riding off into the sunset to live happily ever after.
Can I name Sunset Boulevard for beginning and ending at the same time?
I did - Post #5
Lord of War, the most underrated movie of the last few years.
[Some say, "The only thing needed for evil to prevail is for good men to do nothing.’
They should really say…Evil Prevails."](http://www.youtube.com/watch?v=9d0d6qgsvTw)
Beginning: Desperado
Most of what I could think of has been covered, so I’ll add:
Beginning: Star Trek: First Contact and Star Trek 09
No one has yet mentioned the James Bond movies? Don’t all of them have a spectacular opening sequence (it’s been a while since I saw one)?
Beginning - Wall-E or Wings of Desire
Ending - Aguirre, Wrath of God or Monty Python and The Holy Grail or Evil Dead II(so completely WTF until AoD)
Ending: Empire of the Sun
Beginning:
2001: A Space Odyssey
LOTR: The Two Towers
Ending (I can’t believe I’m saying this)
Back to the Future II (from the moment Doc gets zapped back to 1885)
I was 25! and yes, it was wonderful! It carried over later, on the ride home, down the highway - all the headlights and tail lights and street lamps made me feel like I was flying in my very own space cruiser.
Ending: The Lion King. I had tears in my eyes, the circle of life and all that…
A movie that has a great beginning and a great ending (in the same movie) is Reservoir Dogs. The stuff in the middle is pretty odd, but it starts great and ends great.
The Beginning: Shane
The Ending: Some Like It Hot
Beginning: Jaws
Ending: Wizard of Oz