Casablanca/WMG

Rick can't return to America because he killed someone to save Sam.
It would explain both why Rick can't return to the States, and why Sam is running halfway around the world with him. Back in America, a white person (or group of people) tried to kill Sam, for whatever reason (a robbery, or a lynching, for example). Rick somehow got involved, and in the process of defending Sam, killed the attacker(s). Even though it was an act of defense, blame wound up on Rick and Sam, because it was the 1940s and the cops were racists. So Rick and Sam decided to escape to Europe, and later Casablanca. This theory would fit with what other characters say about Rick. More than once he's said to be someone who often winds up helping the "underdog." Louis speculates that Rick can't return to the States because he killed a man, and Rick confirms this; true, that conversation was sarcastic, but it may also have had some sincerity behind it. "Louis: I've often speculated why you don't return to America. Did you abscond with the church funds? Run off with a senator's wife? I like to think you killed a man. It's the Romantic in me.
 * It's noted in-movie by Louis, where he muses openly about why Rick won't return to America when he can easily afford to:

Rick: It was a combination of all three."

Ugarte is a vampire.
Look at him. Listen to that voice with that accent. It's obvious.

He is an especially powerful vampire, since he is resistant to sunlight. Getting shot was a temporary setback.

Consider that we never see Ugarte...
 * Outside in the sunlight
 * Eating garlic
 * Touching anything silver (he drinks from a glass, but never eats anything at the cafe, because that would require touching silverware!)

He convinced Rick to hold the visas for him with the vampiric power of hypnosis. Note how he kept having to look Rick oddly in the eye now and then, and speak in that quiet silky tone, during the "You despise me, don't you?" conversation. He was hypnotizing Rick. Unbeknown to Ugarte, the Nazis have all undergone training to resist hypnosis, which is why he was unable to use this power to defend himself during his arrest, and had to resort to his gun.

Oh, and those two Nazi couriers? They were delicious.

The entire film is a dream, in which Rick is incepted to join the cause against the Nazis.
The events in “Casablanca” are all part of a dream that Rick has, while passed out in his bar after a night of boozing. Lazlo and his wife do arrive at Casablanca, but Rick does not see them in person; only when they entered his dream, with a team of inceptors trained to trick Rick into subconsciously deciding to resist the Nazis. The team members include Lazlo, Ilsa, Louis, and an unseen fourth member. Their plan is to set up a chain of events that will cause Rick to feel guilt about not helping foreigners pursued by Nazis, force him to finally turn against the Nazis and “help” someone, and give him a sense of catharsis about the whole thing (because positive emotion trumps negative).

First, the unseen fourth team member takes care of the guilt part; he or she is able to change his or her appearance while inside someone’s dream (like Eames). He/she appears first as Ugarte, begging Rick for help before getting “killed,” to solidify a sense of guilt in Rick’s subconsiousness. Then, Lazlo and Ilsa step in. Lazlo tries to convince Rick to “help” him and his wife by appealing to Rick’s noble side, while Isla appeals to his emotion. She tells him about her secret marriage to Lazlo, so that Rick will come to stop blaming her, and feel a catharsis about letting her go. This is crucial in freeing Rick of his bitterness against the world, and so he can stop being self-serving. The fourth team member, meanwhile, returns to Rick’s café in the form of different desperate foreigners (like the Bulgerian woman trying to help her husband) to continue feeding Rick guilt and test whether his actions will change. Louis, meanwhile play thse devil’s advocate. In order to change Rick’s mind about his part in the war, the group needs something to test him against. Louis acts obedient to the Nazis, like Rick, to make Rick question his own actions (or lack of) concerning the war.

Major Strasser was merely a projection of Rick’s dream, representing his fear of the Nazis and the control they have over his mind. When Rick shoots Strasser at the end, he subconsciously “kills” the control the Nazis have put over him with fear. Letting Ilsa go with her husband on the airplane is Rick’s official catharsis, accepting that he cannot have her, and doesn’t need to, because others’ needs are more important than his own desires. Rick will soon wake up after this, because he has now donned his fedora…his totem. He wore it in his other dreams (like the dream where he was a detective searching for the Maltese Falcon). He hasn’t been wearing it for most of this dream, because he chose to forget that he was dreaming. But now that his totem is with him, he will soon be reminded to wake up. And when he does, he will have a new sudden urge to join the Allies against the Nazis.

This movie is the Anthropomorphic Personification of America's decision to enter World War II.

 * Rick is America: living in isolation out of bitter cynicism, professing neutrality but helping people under the table before finally officially moving into action.
 * Ilse is La Résistance (or England): she has emotional ties to Rick (France helped America in the War of Independence; England is America's ally) and appeals to his desire to see his beloved be happy.
 * Victor is the Allies (or La Resistance): once thought dead, he has stepped up in Rick's absence to defend Ilse and appeals to Rick's sense of justice.
 * Strasser is Nazi Germany: no elaboration necessary.
 * Louis is Vichy France: also no elaboration necessary.
 * Ugarte, Annina and her husband are the tiny European countries that never stood a chance against Nazi invasion.
 * I had that exact idea when I realized what "Casablanca" translates to in English.

This film takes place in the same universe as The Maltese Falcon.
Joel Cairo? Casper Gutman? Do these sound like names a person would likely be born with, or more like meaninglful aliases that criminals might pick for themselves? Even Sam Spade sounds a bit too cool to be real; it may well have just been the detective's professional name (like a pen name or a stage name). At the end of The Maltese Falcon, Cairo and Gutman were supposedly arrested, but we didn't see it. That's because they escaped, and a few years later wound up in Casablanca, pretending to be Italians with the new names of Ugarte and Ferarri. (They didn't bother disguising their Hungarian and British accents, since no one asks questions in Casablanca). Sam wound up having to leave America for his own reasons, and once in Europe, started to go by Rick Blaine (possibly his real name all along). Rick has dealt with Ferrari and Ugarte in the past. The events of The Maltese Falcon job are that backstory.
 * Ugarte's comment to Rick, "I hope you are more impressed with me now," makes sense when you consider how pathetic of a criminal he was as Joel Cairo; this time, he actually managed to kill someone and steal something, for once! As Ugarte he shows no obvious signs of homosexuality like he did as Cairo, but we never see Ugarte show any interest in women either.
 * Ferrari knows Rick is secretly a sentimental guy, because he knows about Rick/Sam's past with Brigid.
 * Brigid and Ilsa seem similar--both quiet and innocent, emotional, and even carry themselves simmilarly. The difference of course is that Brigid's personality was an act, while Isla's was genuine. The point is, "Sam" and "Rick" seem to have the same taste in women.

Ugarte was involved with the Italian Mafia.
Ugarte is an Italian name, and many sources say the character is meant to be Italian (Peter Lorre's Hungarian accent notwithstanding). The Mafia absolutely hated the Nazis, which would explain why Ugarte had no moral problems at all with killing the two Nazi couriers. His confusion when Rick is disgusted with his murders, rather than impressed by them, makes sense if Ugarte was born and raised in a world of organized crime, where killing someone might be considered a triumph.