What are some of the best WWII movies?

Band of Brothers.
Stalag 17.
The Great Escape.
A Bridge Too Far.
The Dirty Dozen.

There are a ton, but I just had to mention those first thing.

Adding...

Saving Private Ryan
Dunkirk
Defiance

In addition to all those films mentioned, I also recommend,

Empire of the Sun
Stalingrad
The Big Red One
Black Book
To Be or Not to Be - I recommend both versions.
Kelly's Heroes
Attack (1956)
Battle of Britain
A Matter of Life and Death
Hell in the Pacific
Where Eagles Dare
Hangmen Also Die!

Adding few to the ones already named:

Il generale Della Rovere
Tutti a casa
Jona che visse nella balena
Mediterraneo

Forbidden Games (1952) by René Clément

Ballad of a Soldier is in my top ten of all-time and I think you'd really dig it. Very, very emotional with little of the film actually taking place on the battlefield, but rather on its effects back home.

Band of Brothers isn't a film, but I was thinking about it the other day and it might just be *the* most definitive and perfect film depicting the American side of WWII. Insanely well-made on all fronts.

The Human Condition trilogy is a hefty load, both in terms of run-time and bleakness, but it's absolutely worth it - the third is among my top 5 favorite films of the '60s.

As you were a fan of Spielberg's work in Schindler's List, of course I also gotta recommend two other Spielberg films: Saving Private Ryan (possibly my favorite Spielberg film and a launching point for Band of Brothers - that Spielberg produced - which would do it even better) and Empire of the Sun, which features maybe my favorite child performance ever in Christian Bale and is a much more down-to-earth approach to WWII compared to the other two Spielberg efforts.

Other recommendations in that vein:

• Kanal - Very intimate, gritty Polish film about the Warsaw Uprising.
• Judgment at Nuremberg - The Nuremberg trials. May not count as a WWII film per se, but it was maybe the first major film to discuss the concentration camps and is a strong companion piece with Schindler's List.
• Army of Shadows - A more calculated approach depicting the French Resistance side of WWII. Melville himself (the director) was also part of the French Resistance.
• The Cranes Are Flying - Like Ballad of a Soldier, another Soviet film about WWII that shows the effects of war at home. Like Ballad, incredibly moving and lyrical.
• The Best Years of Our Lives - My favorite film of the 1940s and possibly in my top 50 of all-time. It's about three soldiers returning home from WWII, but for a film made under the Hollywood Hays Code, it's a surprisingly dark, authentic, and affecting look at PTSD and adjusting to the return home.

For some more satirical approaches, I'd recommend The Great Dictator and To Be or Not to Be (1942).

Objective, Burma! (1945) and Ford’s They Were Expendable, released the same year

Not one of the best ever but I really enjoyed Hart's War and thought it deserved a mention.

Band of Brothers
The World at War
Das Boot
The Bridge on the River Kwai
Saving Private Ryan
Dunkirk
Patton
The Thin Red Line
Letters from Iwo Jima
The Book Thief