There are so many great scenes, but one of my personal favorites is when the Germans are singing around the piano and Victor begins the Marseillaise (forgive me if I spelled that wrong). It was just so inspiring.

There are so many wonderfully funny lines, too. "Casablanca is in the desert." "I was misinformed."
"Are my eyes really blue?"
"There is gambling in this establishment!" "Your winnings, sir."

And, naturally, the scene at the airport. Without spoiling this classic for anyone who may not have scene it, it is undoubtedly some of the best-written and best-performed dialogue. Just beautiful.

Edit: And I think that there is one close-up of Ilsa, when Rick first sees her in his bar, that shows Ingrid Bergman to be one of the most breathtaking women ever captured on film.