The Question is secretly Victor Sage, intrepid journalist. With a keen eye for unseen connections and a focus many call obsessive, he makes masked investigation his life's purpose.
The story of The Question begins with investigative reporter Vic Sage. A Randian libertarian, Vic Sage never pulled punches in his on-air interviews. But his public status made it necessary to disguise himself when he needed to investigate a special story. His old professor, Aristotle Rodor had come to him with information regarding an old colleague of his named Dr. Arby Twain. The two had invented a special plastic called Pseudoderm which was intended to be used as an emergency bandage due to its skin-like properties. However, Rodor had discovered that the chemicals in it were actually harmful to humans when applied to exposed wounds. He and his partner had agreed not to use the product, but the partner had reneged on his promise and was attempting to sell it to hospitals in Third World countries despite the health risks.
Vic Sage realized that he wouldn't be able to stop the sale simply by doing a news story. He would need to take action, but had no desire to get himself arrested for vigilantism. So Professor Rodor suggested that he use a mask made of the Pseudoderm to disguise his very public face. Using the blank mask that Professor Rodor devised, Sage was able to stop the sale and extract a confession from Dr. Twain. Vic Sage was conveniently the first reporter to get wind of the story.
This marked the beginning of The Question, though his superhero moniker didn't catch on overnight. When Sage wanted to get information that wasn't available to a reporter, he would put on his featureless mask, spray himself with a color-changing chemical, and go about his crime-fighting business. After he started leaving behind business cards with a question mark on the front, he earned the name by which he is now known. For a while, his superhero antics proved beneficial to his career as an investigative reporter. However, he gradually began spending more time behind the mask than he did in front of a camera.
Eventually, whether from repeated exposure to the chemicals that facilitated his costume change or from the psychological stresses he placed upon himself, Vic started to become a bit unhinged. The more investigating he did, the more he became convinced that there was a vast conspiracy behind virtually every component of commerce, government, and the media. His lack of attention to his job resulted in his being let go from his cushy network job, and he began to spend virtually all of his time as The Question, sometimes going for long periods without taking the mask off or changing his clothes.
Despite being clearly unbalanced, he still managed to gain enough of a reputation as a detective to be recommended by Batman as a new member when the Justice League expanded its roster. While there, he spent the majority of his time hunched in front of a computer screen and worrying the other members. But on a few occasions he was able to provide members of the team with aid, such as the time he helped Supergirl get to the bottom of her nightmares or the time he helped the Huntress go after the man who murdered her father. He even proved instrumental in proving the link between Lex Luthor and Cadmus Labs, bringing himself closer to discovering the truth behind the conspiracy. He also discovered video footage of a parallel universe, which showed that world's version of Superman killing Lex Luthor and ushering in the age of the Justice Lords. Determined to prevent that, he attempted to kill Lex Luthor himself to protect Superman from having to make the choice. This ended badly.
The Question's attempt to kill Luthor failed, and The Question was tortured for information. He proved to be very hard to interrogate, as he ultimately started spouting nonsense when pushed to the point of breaking. However, he was eventually rescued by Superman and the Huntress, and was able to sit out most of the ensuing crises.
Recently, he has taken even more of a backseat role with the Justice League, preferring to focus on what he does best: finding answers to questions. In order to get his message out, he has started writing once again as Vic Sage, operating from an obscure newsblog with barely enough advertising revenue to cover the costs of hosting the site.
To the outside observer, The Question appears to suffer from a complex of progressively worsening neuroses. He is suspicious of everyone, notably digging through the trash of everyone he knows. And he is paranoid to the point of having agoraphobia-type symptoms. He can go days without leaving his rooom, never taking off his mask or bathing.
However, focusing solely on his questionable mental stability gives one a very narrow perspective of his personality. He is, at his core, a very heroic person. Without the use of superpowers, years of training, or a vast fortune, The Question is doing his best to make the world a better place. However, he isn't especially interested in chasing down purse-snatchers or foiling bank robberies. There are plenty of heroes doing those sorts of things. The Question tends to focus on trying to find the root of the problem, rather than treating symptoms.
Despite his proclivity towards making people uneasy, The Question has come through for his teammates often enough that many of them trust him or even consider him a friend. The general consensus seems to be that his heart is in the right place even when his head isn't. Furthermore, The Question is actually /right/ about a lot of his claims. Cadmus really was involved in a conspiracy against the Justice League, and Baskin Robbins really was hiding a secret flavor from the public. It's easy to make fun of The Question when he's in full-on hermit mode, sticking pins into newspaper articles and linking them to other articles with yarn, but the fact remains that he's frequently able to find information that nobody else can.
So no, The Question isn't completely stable. But he's also not insane. If he likes someone, he'll get over his personal issues long enough to help them should they need it, but good luck getting him to change his shirt more than once a week.