When we first meet Rick Blaine (Humphrey Bogart), he is a self-centred businessman apparently out for himself and uninterested in others' lives or problems. He is not selfish, but he is very protective of his interests and is unwilling to get involved in others' business. He refuses to take sides in arguments or do anything that would mean him losing out in any way. Given that the action takes place during the Second World War and his cafe is frequented by Nazi officers, French officials, refugees, and a variety of members of the criminal fraternity "on the make", looking for a free party and loose women, and there were plenty to be found... so this reflects a solid determination.
Rick's desire to remain neutral and his strict policy of non-involvement bear all the hallmarks of existentialism. However, a true existentialist refuses to involve himself in others' lives because this amounts to interference and an existentialist feels he has no right to exert influence on others' lives. So, is Rick acting on the principle of non-interference? I would say that Rick is what I will call a "romantic existentialist", though the effect is largely the same. He is a man who has lost faith in life and especially love. He has lost the desire to consider what is right and wrong because he was hurt, indeed devastated, when the love of his life disappeared from his life, and he is making every effort to ensure he is not hurt or even involved again.
He seeks to avoid being implicated in others' lives not so much because he feels he has no right to influence events, but because he wants no attachments or sentimental responsibility. Actually, he doesn't want anyone to interfere in his life as he has lost faith in others, and as a result appears to have lost the capacity to believe in a cause. Rick is no cold or logical existentialist. We feel that something is eating away at him beneath his brittle shell, and we get our first suggestion that he is in fact something of a romantic at heart when he helps a young lady avoid the corrupt clutches of the chief of police. We see that he is capable of feeling, and that he can see and care about what is right and wrong. This is essential to his appeal, for without this suggestion of humanity he would simply be what he pretends to be— a cold and self-centred opportunist.
Rick wears "existential armor" as a means of coping with what life has thrown at him, but he is reborn when he discovers the truth, that Ilsa's feelings for him were (and are) genuine. This restores his faith and trust, and more importantly his sense of worth. In a sense Ilsa is the braver and more tragic of the two. Believing her husband to be dead, she embarks on a relationship with Rick, a relationship they both find joyous and fulfilling. However, on discovering her husband Victor is in fact alive, she severs her relationship with Rick out of loyalty and respect for her husband. Ilsa's situation is more complex and perhaps even more painful than Rick's as she turns her back on passion and romance in favour of a more admiring and respectful form of love. This would appear to be a victory for principle and spirituality over spontaneous and heartfelt passion— a difficult choice to make and then live with. Yet Ilsa knows the truth about her feelings for Rick, and doubting these feelings is the real source of pain for him. He has come to believe that what meant so much to him was, in fact, false and without basis, and this has caused him to doubt sincerity and motive in general. Of course, when he discovers that he was indeed loved his sense of self worth and self-respect is restored and he is ready to play a part in others' lives once again.
Moreover, Rick displays a selflessness born of love and respect. He puts Ilsa and Victor's fates above his own, thereby also putting the war effort above his own security and turning his back on his "existential crisis" in which he had come to believe in nothing but his own survival. Major Strasser and the nazis may represent the amoral imposition of one will over others' while Victor Laszlo represents the voice of reason and principle. Defiant, courageous and inspiring in the face of overwhelming opposition. Ilsa puts principle above her feelings to follow Victor, and eventually Rick makes a similar choice, putting thoughts of others and belief in principle above personal considerations— a choice made for humanistic reasons and out of self-respect and respect for others. Might this also reflect America's decision to finally get involved in WW2? It is indeed a very real possibility as Hollywood always exercised its voice.
As I have suggested above, I'm not sure that the reasons for Rick's outlook on life can be described as truly existential, though the resultant non-involvement is the same. Other elements— the lack of religion, the way in which the various characters' fates are interdependent, Louis' determination to gain the maximum benefit for himself, the juxtaposition of amorality and principle, the humanistic approach to problems faced by society— these are all classic existential elements. What makes the film all the more special is the fact that all this is combined with romance, compassion and of course humor. An existential drama which is both thought-provoking and entertaining is rare and is to be savored.