Most people think that the dawn of the superhero and the costumed crime fighter was in 1938 and 1939, when comic books started appearing and characters like Superman and Batman were first being published. The truth is that those comic book characters owe a lot to what was happening in the 20s and 30s in newspaper comic strips and are far from the first costumed heroes to appear.
Action and adventure comic strips had existed since the 20s and were quite popular. Some notable examples are Hal Foster's Prince Valiant, which began in 1937, and Milton Caniff's Terry and the Pirates, which began in 1934. The storylines spanned months and years, put the characters in real danger, and always included incredible cliffhangers. The artwork was exquisite, and in my opinion was far better than anything published in golden age comic books.
There were also what were called "crime comic strips," which dealt with policemen and even costumed vigilantes. One of the most famous crime comics was Dick Tracy, who first appeared in 1931. Created by Chester Gould, he not only fought common criminals, but also organized crime. He had his share of fancy gadgets to help him, which he used to deal with his large and very colorful rogues gallery. Not only was he doing all this 8 years before Batman arrived on the scene doing similar things, but he did it entirely in his newspaper comic strip. The only "comic books" Dick Tracy appeared in were reprints of his comic strip adventures. He didn't get a comic book with original material until the 80s.
Of course, Dick Tracy was an actual plainclothes policeman and not a costumed vigilante like Batman. The newspaper comic strip page did have Lee Falk's The Phantom, though, who was. First appearing in 1936, three years before Batman, The Phantom always wore a very distinctive costume and had a secret identity. His real name was Kit Walker, and he was 21st in a long line of men who wore the Phantom costume and fought crime.
Over time, themes from adventure comics such as the secret identity, colorful rogues gallery, skin-tight costume, and handy crime fighting gadgets would become common themes in the superhero comic book genre. They didn't start with comic books, though, but with newspaper comics. Interestingly, both Dick Tracy and The Phantom still run in newspapers today, though with different writers and artists.
More info:
Dick Tracy at Don Markstein's Toonopedia
The Phantom at Don Markstein's Toonopedia
Chester Gould at Lambiek Comiclopedia
Lee Falk at Lambiek Comiclopedia
Dick Tracy at GoComics, currently drawn by Joe Staton and written by Mike Curtis.
The Phantom at Comics Kindgom, currently drawn by Paul Ryan on dailies, Terry Beatty on Sundays, and written by Tony DePaul."