During the summer of 1989, everyone was swept up in Batmania, the term given to the film's insane success at the box office, with merchandise, and fans who literally shaved the bat signal into their heads. (Source)
The biggest Batman—and Batwoman—fans could wear a Batman tank top and Batman bike shorts with a Batman lapel pin and ride their bike (what, no Bat-Bike?) to a friend's house to play cards with Joker-branded cards while drinking coffee from a Bat-mug under the watchful glare of a Batman poster on the wall and maybe, during the card game, win enough money for a $500 pair of Batman and Joker figures. (Source)
It's a lot of Bat-gear, and we didn't even mention the action figures, video games, and magazine covers for the obsessive collectors. (Source)
As an aside, Jack Nicholson proved smarter than Joker when he agreed to play the role for less than his normal fee, but with a portion of ticket sales and merchandising. (Source)
Batman rejuvenated a long-dormant franchise. This version of the character would star in three more films, and be played by three different actors—Keaton, Val Kilmer, and George Clooney. Laid to rest after Clooney's flop Batman and Robin in 1997, the franchise would be resurrected by Christopher Nolan and Christian Bale with Batman Begins in 2005. Ben Affleck would even don a batsuit in Batman vs. Superman: Dawn of Justice in 2016.
So yeah, Batman is pretty insanely popular. We're surprised there isn't a real-life Bat-Signal to alert fans whenever new Bat-news breaks.