Since you wouldn't want comic book heroes to age like their readers, but instead appeal to a new generation of young readers, most comic books use what is a called a Floating Timeline, in which the characters are always the same age:
Any dates given within the comic are not relative to the publishing date of the comic (i.e. "10 years ago" means "10 years before you read this"). This device enables publishing companies to continue to use their characters for as long as they wish without changing them significantly.
This, of course, means that character histories fluctuate over time:
in 1960s comics by Marvel Comics, the character the Thing states he fought in World War II. However, in comics in the 2000s (decade), the Thing states that the idea of him fighting in World War II is ridiculous, as he would have to be much older.
Batman's origin often shows his parents murdered in 1930s or 1940s fashions, while the adult Bruce Wayne clearly lives in the present (this is shown in fashion and technology). In The Return of Bruce Wayne #5, Batman travels in time to shortly after his parents were murdered. The 1930s-style clothes and cars are explained by a character who informs him that "retro is big this year," keeping the iconic image but being vague about the actual year.
Of course, sometimes you want to show the heroes aging. In Batman Beyond, set in futuristic Gotham, Bruce Wayne is an aging retired Batman, mentoring the younger generation. However, this isn't a case of Batman aging, as much as a different continuity that starts with an elderly Batman.