Popeye; First appearance: Thimble Theater (comic strip), January 17, 1929. Popeye quickly became the featured character and later the strip took his name.
First appearance at the movies: Popeye the Sailor. The Fleischer cartoons starting in 1933 and continuing, off and on, for twenty-five years.
First appearance in radio: 1935
First feature length film: Well, I'm going to give two dates. The Fleischer studios produced 108 Popeye cartoons, 105 in black and white. The remaining three were two reelers (double length, about a half hour), starting with Popeye the Sailor Meets Sinbad the Sailor in 1936. However, a true live-action feature length movie had to wait until the Robert Altman Popeye with Robin Williams in 1980.
So... Popeye went from origin to cultural icon in the movie theaters (and eventually on tv) in just a few years, but waited many years for a live action film. And is still waiting for a good one.
Superman. First appearance: Action #1, June 1938
First appearance at the movies: Superman The Fleischer animated seres 1941-43.
First appearance in film: Superman: A serial in 15 chapters, 1948
He was at the 1939 New York World's Fair (in 1940), on the radio in the 40s and on tv in 1952.
So... Superman went from origin to being on the big screen in three years, but waited nearly ten years for his first live action film serial.
Batman (Bob Kane): First appearance: Detective Comics #27, May, 1939
First appearance in other media: As a comic strip in 1943.
First appearance in the movies: Batman, a 15 part serial in 1943. A second movie serial followed in 1949.
First appearance on tv: Batman, the 1966 Adam West-Burt Ward show, fondly remembered by it's fans for the theme song and the delicious guest villains.
So... Batman went from origin to being on the big screen in four years.
Archie: First appearance: Pep Comics #22, 1941
First appearance on tv: The Archie Show, 1968. 17 half-hour shows in two 11 minute segments, introducing the song "Sugar Sugar".
First appearance as live-action tv movie: Archie: To Riverdale and Back, 1990
ETA: The Wiki page failed to mention the Archie Radio series, starting in 1943, but this page does: Archie Andrews
So... I would be remiss in not mentioning the spinoffs (including a various other animated series and Sabrina The Teenage Witch movie and then tv show) and cultural impact of Archie and his pals. Still, his comic book fame never quite translated to other media (though, as added above, his radio series lasted more than ten years until 1953).
Captain America (Golden Age): First appearance: Captain America Comics #1, March 1941
First appearance on the big screen: Captain America, 1944, the most expensive serial that Republic made, and it's last superhero entry.
So... while Cap was very popular during WWII, interest in him faded after the war and remained dormant until the Silver Age revival.
Spiderman: First appearance: Amazing Fantasy #15, August, 1962
First time on tv: Spider-Man, animated series 1967-1970
First time as live action on tv (not counting his appearances on The Electric Company): The Amazing Spider-Man, 1977-1979.
First time in a live-action movie (not counting the made-for tv pilot, above): Spider-man, the 2002 Sam Raimi film.
So... Spiderman took five years or so to gain enough cultural cred to get his own cartoon show but, like Popeye, a live-action feature length film would take many years.
Iron Man: First appearance: Tales of Suspense #39, March 1963
First appearance on tv: One of five of The Marvel Superheros in 1966. Then next appeared as a guest star on Spiderman's 1980s series.
First appearance in a live-action movie: Iron Man, in 2008
So... while Iron Man rode the wave of Marvel's popularity, he was always part of a group effort and didn't get his own movie until forty-five years after being introduced.
Captain America (Silver Age): First appearance: Strange Tales (a Human Torch story), Nov, 1963. Formally introduced in The Avengers #4, March, 1964.
First appearance on tv: One of five of The Marvel Superheros in 1966.
First appearance in a made-for-tv movie: Captain America, 1979, with a sequel that same year. I doubt it was intended as a direct-to-video release, but it wasn't all that good and disappeared quickly. There was an unrelated Captain America movie in 1990 that, too, went direct-to-video.
First appearance on the big screen: Captain America: The First Avenger, 2011. One of the successful prequels to The Avengers movie.
So... like Iron Man, Cap was packaged with other Marvel heros but never really caught on outside his comic book until nearly fifty years after his reintroduction.
Judge Dredd: First Appearance: Second issue of 2000 AD, 1977
First appearance on the big screen: Judge Dredd, 1995, the movie with Sylvester Stallone and Max von Sydow
So... a well received British character makes his way to the movies with a big name and a big budget, and lands with a thud.
Batman (Frank Miller) aka The Dark Knight: First appearance: 1986
First appearance on the big screen: Batman, 1989, the Tim Burton movie.
First appearance in animation: Batman: The Dark Knight Returns: September, 2012
ETA: I neglected to mention Batman: The Animated Series, 1992-1995. While not specifically The Dark Knight, the show certainly owed far more to Miller than Kane; far removed from 60s camp and darker than the Burton movie. The first year is my favorite incarnation of The Batman.
So... The Dark Knight, perhaps the most successful reinvention in comic book history since the Golden Age heros on Earth-2 were adapted to the Silver Age heros on Earth-1, took just a few years to transform one of the most well-known comic book superhero into a matinee idol.
Watchman: First appearance: Limited series starting September 1986
First appearance on the big screen: Watchman (2009)
Tank Girl: First appearance: Deadline, 1988
First (and only) appearance in the movies: Tank Girl, 1995
So... an underground comic took a few years to percolate before a movie came out to mixed reviews and lost a lot of money for its backers.
What does this tell us?
I hope this small sample of list of English-language comics turned into movies adds some perspective to Disney's buyout of Marvel and Warner's ownership of DC. Basically, with few exceptions, comic books were a great way to introduce the American public to a character. Then came tv, movies, CGI and big budgets. Comic books writ large can make it in the movies, but only if the characters are well established and their backstories well-known.
Comic books used to drive people's perception of the heros. Spiderman's unsung hero was Steve Ditko, who gave the hero a distinctive look. Don't step on Superman's cape. The Dark Knight is an image as well as an action. Captain America never gives up.
Now... not so much. We have remakes and reimaginings. I don't particularly begrudge anyone for trying, but they don't succeed all that often. I'd like plenty of movies and tv shows much better if they gave a nod to the influences rather than trying to reinvent a character and tripping over their cape.
But that's just me.