When you're talking about a movie that's widely considered to be one of the best ever made, of course you're going to have a large fan base. However, Casablanca aficionados are quite a different crowd than, say, your Star Trek fanatics. You're not going to find too many Casablanca costume parties, you won't see Renault lookalikes walking around Comic-Con, and you'll never bump into a person sporting "Rick ears." No, Casablanca fans are fewer (mainly because most of the original fans have died out by now), and they're generally a tad classier.
Starting in the 1950's the film began to take on cult status. And during the 60's, a new generation of antiwar folks would stand up and cheer when the patrons at Rick's defied the Nazis and sang "La Marseillaise." Harvard even had a Bogart festival every semester that culminated with the screening of Casablanca. Today, colleges around the country have regular showings of the film, with lines around the block to get in. (Source)
Because this is such a famous and classic episode of cinema history there are plenty of online fan sites dedicated to remembering it. Maybe none of them amount to a hill of beans, but let's round up the usual suspects: