Longest Running
Superman made his first appearance in Action Comics in 1938, and has had a new issue come out every month since then. He was also the first comic character to appear on celluloid, both with the first TV drama and, some decades later, the first superhero movie. Whatever you may think of the Man of Steel and his storyline, he's got seniority on all the competition.
Most Successful Movie
This one's a little open to interpretation. Batman is the clear single-film winner, with "Dark Knight" raking in a total gross sales of over 100 million dollars more than the number two guy. However, three of the top five grossing comic book movies feature Spider Man, making Spidey a higher grosser in total than Bruce Wayne's alter ego.
Best Selling
According to MyComicShop.com, "The Uncanny X-Men" is the best selling comic book series of all time, selling more total issues than several series that have been running for over a decade longer. The X-Men is an ensemble cast comic, making it hard to nail down which member of the crew qualifies as the "best." Based on the popularity of spin off comics, t-shirt sales and general fandom, Wolverine can be argued as the driving force behind the success of this comic series.
Most Critical Acclaim
Although graphic novels have been taken increasingly more seriously since the mid 1990s, the comic to win the most critical acclaim remains the 1986 release Watchmen" by Alan Moore. It's the only graphic novel on Time Magazines list of the top 100 novels, and many experts credit the recent respect for comics as literature to the release of this comic. "Watchmen" is another ensemble story, though many fans point to either Rorschach or Ozymandias as personal favorites.