|Not a bourbon I drink...|
SAM: Yes, boss?
RICK: If it's December 1941 in Casablanca, what time is it in New York?
SAM: Huh? My watch stopped.
RICK: I bet they're asleep in New York. I bet they're asleep all over America.
There's a scene-within-a-scene here, a flashback montage of Rick and Ilsa's romance in Paris. A lot of champagne is poured in this flashback, and we actually see Rick and Ilsa drink some, at the beginning and at the very end. (As far as I can tell, the one sip Ilsa takes in this sequence is the only drinking the character does in the entire movie. As if to symbolize her attitude toward drink, Ilsa closes the scene in the Cafe Belle Aurore by knocking over a full glass of champagne.)
When the flashback ends, Rick's glass is empty and the bottle has only an inch or so of bourbon in it. When Ilsa intrudes on his misery, Rick pours himself another shot. He downs nearly the whole thing in one belt, too: that's how unhappy he is. Rick hardly touches a drop before this scene; for the rest of the movie, nearly every scene he's in he's holding a drink. (Incidentally, this scene ends with Rick downing another shot of bourbon, a shot we haven't seen him pour.)
The next booze shot (so to speak) takes place next morning at the Blue Parrot, the cafe owned by Signor Ferrari (Sidney Greenstreet). Ferrari offers Rick a drink, to which Rick responds, "I never drink in the morning." Ferrari pours him a drink anyway, from a fresh bottle. Scorning Ferrari's hospitality, Rick walks away without touching the drink. (Ferrari doesn't have much luck with his guests; immediately after Rick leaves he makes, with his own hands, a cup of Arab-style coffee for Ilsa―who sets it aside without even inhaling the aroma. She does thank him for it, though.)
Back at the bar, a couple of extras down drinks while Rick and Louis sip cognac―once again, Louis leaves his drink unfinished. More cognac is poured (and some actually drunk) by Karl and two extras in a comedy-relief bit. Rick finishes the cognac he began drinking with Louis, then sets out to help Bulgarian refugees Jan and Annina Brandel (Helmut Dante, Joy Page) win at roulette; Victor and Ilsa appear at the club and order cognac, apparently tired of all the champagne they didn't drink the previous evening.
Of course they don't drink anything.
After the roulette incident Rick pours himself another cognac (his third of the evening), but only has one sip before Victor drags him away from it. Regardless of the purity of his soul and his politics, this guy sure is a killjoy. At contemporary prices, he and his wife waste several hundred dollars' worth of perfectly good alcohol during the course of the film.
At this point the action starts moving fairly aggressively and the drinks stop flowing. After Rick and Ilsa become lovers again there are a bottle and full glasses of champagne on the table in front of them as they talk, but neither drinks (though Rick does toast Ilsa, one of several times he says "Here's looking at you, kid" to her). The noble Victor does finally stoop to taking an honest swig of elixir, however: after cutting his hand while escaping from the police, he allows Rick to pour some cognac into him. It's only one sip, though, and clearly For Medicinal Purposes Only. (It's no wonder Ilsa prefers Rick to this bloodless shmoo.) It's ironic, I suppose, but Victor is the last person to drink alcohol in the film.
(Tomorrow we'll wrap all this up with some overall thoughts about Casablanca as a movie and as a cultural artifact.)