For your viewing pleasure

Try:
T-Men
He Walked by Night
Raw Deal (Not the Arnie one)
The Big Combo
The Blue Dahlia 
The Glass Key
Out of the Past
Asphalt Jungle
Laura
The Killing 
Murder, my Sweet (aka: Farewell my lovely)

All stunning stunning films, brilliantly directed, played, wonderfully crafted films. Noir is all about style and these are among the most stylish of this incredible genre.

If you find it a little hard to appreciate what you might perceive as being dated or something, think about modern noir and films today that you may like that are directly influence by noir and work you way back from there.

Most of the Coen's:
Blood Simple
The Big Lebowski
Millers Crossing
Fargo
No Country For Old Men

Also:
A History of Violence
Memento
Grifters
Reservoir Dogs
Blade Runner
LA Confidential
The Usual Suspects
The Dark Night

Noir is usually centered around an unreliable narrator or a character with a tragic flaw that will eventually snowball into something catastrophic. If you learn to appreciate this genre it is one of the most fascinating and exciting genres within cinema and there is a wealth of amazing films there to be discovered.

Enjoy