12 Monkeys isn't your typical Hollywood space adventure. Its protagonist isn't out to defeat a dark lord or save a princess. Instead of epic space battles, it features grim, dirty fist fights. It even lacks a comedic sidekick. And before you ask, no, Jeffery Goines does not count as this movie's Olaf. That's just too disturbing to consider.
The film lacks any interest in being typical Hollywood fanfare, so it's no wonder that it doesn't have much fanfare following it. People don't have 12 Monkeys-themed weddings, there isn't a toy line of James Cole action figures, and we haven't seen anybody don one of its characters for some Comic-Con cosplay. And that last one is a real shame because Cole's futuristic hazmat suit would be epic. (Seriously, cosplayers, get on that.)
Instead, 12 Monkeys is what would be considered a cult film. What's a cult film? AMC's Filmsite provides a useful answer for that question:
Cult films are usually strange, quirky, offbeat, eccentric, oddball, or surreal, with outrageous, weird, unique and cartoony characters or plots, and garish sets. They are often considered controversial because they step outside standard narrative and technical conventions. They can be very stylized, and they are often flawed or unusual in some striking way. (Source)
Sound familiar? That's 12 Monkeys with all the Ts crossed and Is dotted. Now that we think about it, that's Gilliam's entire career in a nutshell.
These films have what is called a cult following, a group of people who fiercely love the thing. Sometimes, these groups can develop into full-on subcultures—think your Trekkies or Rocky Horror Picture Show interactive movie showings—but that's not necessary to be considered cult.
As it is, 12 Monkeys barely makes the cult cut. It was critically acclaimed, did modestly well at the box office, and even had a few award wins. As time went on, though, it began to drift to the corners of our cultural consciousness with a few dedicated Gilliam fans preaching its awesomeness from the mezzanine.
Today, the film isn't as well known as, say, Star Wars, Star Trek, or even Planet of the Apes, but thanks to the internet, all fandoms have a place to call their own. Writers on pop culture websites like A.V. Club and Den of Geek have written articles to rekindle interest in Gilliam's mind-bending masterpiece. 12 Monkeys even proved recognizable enough to receive a remake, courtesy of the SyFy Network's television show, and with that came the subsequent wikis, Facebook fan pages, and so on.
Not that this says anything about 12 Monkeys in particular; Hollywood will remake anything with a pulse.