The paranormal
Clearly, a major theme in Ghostbusters is the paranormal and the world of ghosts. From the first scene of the film, the city of New York has been set upon by some spooky and unworldly ghosts. The Ghostbusters, as parapsychologists and scientists of the occult, are interested in looking into other dimensions to find real relationships between the real world and the supernatural.
Throughout, they believe in the supernatural events happening around them, but other people cannot quite believe that what they purport to do is real. In this way, they are members of a subculture of people who believe in the unseen, the uncanny, and the mystical.
Judgment Day
The threat to mankind at the center of the film is not just that the ghosts in the film are annoying or are taking over the city, but that there is a larger demonic presence, Gozer, that is attempting to get through the portal of Dana's apartment building and bring about the destruction of the world. Apparently, there was a famous cult leader who, after World War I, decided that mankind did not deserve to exist anymore and called upon the forces of Gozer to wreak destruction on the world and its inhabitants. Egon and Winston discover that this is the force behind the demonic events taking place in the city and realize that Gozer wants to bring about "Judgment Day."
Business
When their grant gets rescinded and they are fired from their positions at Columbia, the group of parapsychologists must find a new way to make money and continue their work. They decide to convince Ray to take out a third mortgage on his family home so they can start the Ghostbusters. Shacking up in a dilapidated fire station, they set to work building their business, but at first, it's pretty slow. Just as they are on the brink of financial collapse, they get their first job, and things only pick up from there. Soon enough they have a thriving business as Ghostbusters. Thus a major structural arc of the film is watching the Ghostbusters become successful businessmen.
Teamwork
Part of the Ghostbusters' skill and virtue as a team is their ability to work closely together. Each of them brings different skills to the table; Peter is very practical and ambitious, Ray is earnest and motivational, and Egon is the brainiest of them all. Teamwork is essential to their success, and at the end, when they have exhausted all their options for defeating Gozer, they decide to "cross streams," meaning they pool together the streams from their proton packs to once and for all destroy the portal to the demonic world.
Dating
While it is not a major theme, the love story between Peter and Dana is important to the plot of Ghostbusters. Indeed, Peter's attraction to Dana is what leads Peter to take the haunting in her apartment so seriously, and he is dogged in his romantic pursuit of her. While she does not immediately take to his sarcastic ways, when he shows up at Lincoln Center and watches her rehearse as a cellist, waiting outside for her and making jokes at her date's expense following the rehearsal, she begins to fall for him. When he goes to their date, however, she's been possessed by Zuul, and he has even more of a need to save her from the haunting in her apartment. By the end, he saves her from possession and death, and they kiss triumphantly.
Living Outside the Rules
The Ghostbusters provide a much-needed service to New York City—saving lives and exterminating ghosts all over—but they are rarely on the side of rules and order. True mavericks, they take matters into their own hands and decide to run a business their own way. Indeed, they are fired from Columbia for being too outside the traditional rules of academia. Their work as "parapsychologists" is deemed "pseudoscience" by the powers that be. This skepticism and dubious status follow them into the business world, and they face the same limitations as the Ghostbusters. While people use them and take them seriously to extract ghosts from their homes and businesses, the Ghostbusters ruffle the feathers of Walter Peck and the EPA, who does not believe that their services are real, and think instead that they force people to hallucinate things in order to help business. Thus, while they fulfill services, the Ghostbusters still contend with rule-makers who think they are illegitimate.
Heroism
While the Ghostbusters have many detractors and skeptics, they become heroes to the people of New York, appearing on the news and becoming local celebrities of sorts for the service they provide to the city's residents. When they go to Dana's apartment to do the final purge of the demonic presence afflicting the city, a large group of fans and admirers assemble, cheering on the Ghostbusters and counting on them to save the city. When they do close the portal and excommunicate Gozer from the city, they emerge from the apartment building to grateful cheers and ecstatic celebration. Once losers with no prospects and little to show for their work, the Ghostbusters become heroes by the end of the film.
