My top 5 would have to be:
Memento
Dial M For Murder (sorry, but no top 5 list would be complete or accurate without at least 1 Hitchcock flick. I might be willing to swap this for The Birds. Might.)
Citizen Kane
The Scarlet Pimpernel, and, believe it or not, I think I’d have to go with. . .
The original Rocky
Airplane!
Shakespeare in Love
Citizen Kane
The Red Violin
Hero
I particularly like the transition from farcical to deep to beautiful.
Well, if our boy is gonna die after viewing these 5 movies, don’t you think he’s gonna appreciate if we give him as much time as we can?
I figure you might as well die laughing:
This is Spinal Tap
Airplane!
The Last Dinosaur (strictly a so-bad-it’s-campy turkey)
Withnail & I
Flirting With Disaster (and keep it on through the closing credits)
Ikiru
Okay, my five must see before you die:
The Shawshank Redemption
Bull Durham
Office Space
Dances With Wolves
Brokeback Mountain - as a bonus, if you’re dying, you won’t spend the next four months of your life wondering when you’re going to get over this film.
I read this as a list of movies I’D want to watch if I knew I was dying…
Caveman
Time Rider
Sister Act…2
Mortuary
Parents
I kid, I kid…
The infamous Ardred’s list:
Highlander
Dune
Excalibur
Ladyhawke
Flash Gordon
My list:
The Usual Suspects
Memento
Being John Malkovich
Moulin Rouge
Star Wars
I’d go with:
Breaker Morant - A simply awesome court-martial and military adventure/drama set during the Boer War. It will stick with you for a long, long time.
2001: A Space Odyssey - Wondrous and moving, far ahead of its time.
The Lord of the Rings trilogy - A brilliant accomplishment, thrilling and fun, even better in some ways than the books (D&R, but I believe it…)
Groundhog Day - Everyone should see it at least once. The smartest, most worldly, philosophical yet funny comedy ever made.
The Incredibles - Pixar practically could have closed up shop after they made this, it’s so damn good (but I’m glad they didn’t). Funny, amazing, sly and great eye candy. Lives up to its title.
Oh, and just one more…
Raiders of the Lost Ark - The quintessential action/adventure movie, it just gets better with every passing year. (Indy #4 won’t even come close, I’m afraid).
Showgirls!
Natural Born Killers
Cool Hand Luke
To Kill a Mockingbird
Raiders of The Lost Ark
Star Trek II The wrath of Kahn
Amores Perros (Mex.) 2000
Bottle Rocket 1996
Goodfellas 1990
Life is Beautiful (It.) 1998
Shawshank Redemption, The 1994
If you have enough life for 5 more:
American Beauty 1999
Clockwork Orange, A 1971
Godfather, The 1972
In the Name of the Father 1993
Memento 2000
Finally, if you can’t get your hands on any of the above:
Game, The 1997
Pulp Fiction 1994
Shallow Grave 1994
Swimming With Sharks 1994
Trainspotting 1996
True Romance 1993
Here’s my weird list:
Trainspotting
The Iron Giant (thanks previous poster who listed it)
Clueless
Father Goose
The Tuskegee Airmen
Edit: I have to list these too:
Chocolat
Finding Forrester
Much Ado About Nothing (directed by Kenneth Brannaugh)
Enchanted April
Dune
Analmaniacs 2
Suck It Dry 7
Weapons Of Ass Destruction 5
Splendor In The Ass
Where The Boys Aren’t
Indulge in some Cate Blanchett-y goodness…
Paradise Road
Oscar and Lucinda
Elizabeth
Bandits
Babel
If you’ve only got time enough to see five movies before you die, I suggest some real-life fun. Then again, I remember how the ep ended when Homer Simpson found out he wasn’t going to die of fugu poisoning …
Fletch
Bonfire of the Vanities
Battlefield Earth
The Gods Must Be Crazy
It’s Pat: The Movie
Nobody wants to die. Watching these might encourage you to welcome it. 
A Man For All Seasons
2001: A Space Odyssey
Guess Who’s Coming To Dinner
American Graffiti
To Kill A Mockingbird
That’s my $.02 worth…