Don't know what to rent?  Let me make some suggestions.

12 Monkeys
21 Up (and all the rest of them)
25th Hour
28 Days Later
About a Boy
Affliction
Alien
All About My Mother
All the President's Men
Almost Famous
Amelie
Apocalypse Now
Beetlejuice
Being John Malkovich
Blazing Saddles
Blood Simple
Blow Out
Bottle Rocket
Brazil
Breaking the Waves
Brokeback Mountain
Burden of Dreams
Butch Cassidy and the Sundance Kid
Children of Men
Chocolat
Cinema Paradiso
Clear and Present Danger
Close Encounters of the Third Kind
Code 46
Collateral
Cookie's Fortune
Cool Hand Luke
Crooklyn
Crouching Tiger, Hidden Dragon 
Dancer in the Dark
Das Boot
Deliverance
Delicatessen
Dirty Harry
Dog Day Afternoon
Eight Men Out
Election
Endless Summer
Face/Off
Fallen
Fargo
Fear and Loathing in Las Vegas
Fight Club
Frailty
Freeway
Glengarry Glen Ross
Goodfellas
Grindhouse
Grizzly Man
Hard Boiled
Harry Potter and the Sorcerer's Stone, et al
Head-On
House of Sand and Fog
Incident at Oglala
Insomnia (Norwegian/Swedish version)
Into the West
Jaws
Ju Dou
Kikijiru
Kill Bill 1 & 2
Kramer vs. Kramer
La Femme Nikita
Lone Star
Lost in Translation
Ma Vie En Rose
Magnolia
Magnum Force
Marathon Man
Matewan
Me and You and Everyone We Know
Memento
Midnight Cowboy
Midnight Express
Miller's Crossing
Million Dollar Baby
Mrs. Brown
My Best Fiend: Klaus Kinski
My Neighbor Totoro
Naked
Night on Earth
No Country for Old Men
Ocean's Eleven
Odessa File
Once Were Warriors
Out of Africa
Out of Sight
Outside Providence
Paris, Texas
Passion Fish
Pee Wee's Big Adventure
Ponette
Predator
Prospero's Books
Pulp Fiction
Raiders of the Lost Ark, et al
Raise the Red Lantern
Raising Arizona
Reservoir Dogs 
Rosemary's Baby
Run Lola Run
Rushmore
Secrets and Lies
Se7en
Sexy Beast
Shaun of the Dead
Shallow Grave
Silkwood
Smilla's Sense of Snow
Smoke Signals
Snatch
Sophie's Choice
Spirited Away
Spoorloos (The Vanishing)
Stranger than Fiction
Sudden Impact
Superfly
Swimming to Cambodia
Tampopo
The Accidental Tourist
The Big Lebowski
The Bourne Identity, et al
The Boys from Brazil
The City of Lost Children
The Conversation
The Cook, The Thief, His Wife, and Her Lover
The Dead Zone
The Deer Hunter
The Departed
The Devil's Backbone
The Endless Summer
The Enforcer
The Fifth Element
The French Connection
The Graduate
The Good, the Bad, and the Ugly
The Hairdresser's Husband
The Hours
The Hunt for Red October
The Killer
The Killing Fields
The Last Emporer
The Life Aquatic with Steve Zissou
The Manchurian Candidate
The New World
The Pianist
The Piano
The Pillow Book
The Professional
The Royal Tenenbaums
The Secret of Roan Inish
The Shining
The Silence of the Lambs
The Sixth Sense
The Station Agent
THe Story of Qiu Ju
The Sweet Hereafter
The Thin Blue Line
The Usual Suspects
The Untouchables
Three Days of the Condor
Three Kings
Thunderbold & Lightfoot
Tie Me Up! Tie Me Down!
To Be and To Have
To Sir, With Love
Traffic
Trainspotting
True Romance
Truly, Madly, Deeply
Unforgiven
Volver
Whale Rider
When We Were Kings
Wild at Heart
Withnail and I
Witness
Women on the Verge of a Nervous Breakdown
Wonder Boys
Young Frankenstein