The Shadow was a well-received comic when it debuted in 1973. It was, of course, a comic adaptation of the original pulp fiction character's adventures and indeed took place in the 1930's as the original stories did. Writer Denny O'Neil, editor Len Wein, and artist Michael William Kaluta created a handful of stories that captured, as much as one probably could in the comic book form, the look and feel of pulp fiction. The Shadow and his assistants made for entertaining reading as they solved mysteries and fought criminals; but somehow, the characterization didn't tend to add up to much. Like the Golden Age heroes who came immediately after them, the pulp heroes were long on slam-bang action, but pitifully short on the qualities that modern readers often look for in ongoing-series characters - the backstory, the motivation, the fallibility, etc. (Not that this has ever hurt the popularity of many such adventurers.)
Ultimately, the Shadow series comes off as a very competent read, but not much more - the Shadow and his companions have good adventures, but we don't find ourselves wanting to stick around for more of the same. And unfortunately, much of the series's popularity initially had to do with Kaluta's art style; he only stuck around for five issues, leaving the rest to such artists as Frank Robbins and E.R. Cruz. The series only lasted twelve issues.
You can see a full gallery of The Shadow cover images here