As with several genres adapted to rpgs, pulp gaming presents a little bit of a problem going from the inspirational fiction to the gaming table in that pulp fiction/movies/comics tend to be about solo heroes or a primary hero and sidekicks but rpgs tend to be about a group of equals. It's perhaps reasonable to play Indy plus Short Round and Sallah or even Doc Savage plus his Fabulous Five for one story arc, but it might not be as desirable for a long campaign.
On the other hand, a group composed of Indiana Jones, Jake Cutter (from Tales of the Gold Monkey), and Sam Spade may be fine for some, but seems to be less satisfying to me for a long-term campaign, because the characters don't see cohesive.
The solution seems to me to build a group wherein the characters are roughly equal, but each has their own specialty, and they have the same theme/subgenre. Sort of like if the Fabulous Five didn't have a Doc Savage to outshine them. There are really more examples of this in comics rather than the pulps (though that may just be my knowledge of the pulps is less). Check out the Challengers of the Unknown:
Having the same subgenre is important for keeping power levels similar. Having the same sort of theme is important for helping support their reason for staying together as a group. Of course, both of these can be stretched a bit.
Sometimes teams are brought together or forced to stay together by an outside force. DC Comics' The Secret Six and Suicide Squad (either the Silver Age nonsupers version or the later supers versions) are examples of this, but so is the more eccentrically charactered League of Extraordinary Gentlemen. For that matter, the Avengers, particularly in the Ultimate Universe and the CMU start out like this too.