I was thinking about this earlier and had a few ideas in quick succession about. This list is specifically based on "kitchen sink" settings like Marvel and the old 52 DC. I can't guarantee that it'll make your setting great and memorable but it should convey a sense of familiarity while preserving some surprises. For now, I'm just going to focus on organizations that should be present in such worlds.
The TeamThis is the main superhero group of the world, known by virtually everyone, and influential on a global stage. It contains a variety of heroes; magicians, superscientists, people who can punch really good, etc. A good group size is about 5-9 heroes here, most of whom should have a noteworthy career outside of the group. Also, consider who/what the heroes are and how being a global celebrity might shape public opinion. If a member is a robot or an alien, expect to see more acceptance of robots or aliens, respectively.
Examples of these organizations in comics: The Justice League, the Avengers
The Old TeamFounded back in dubya-dubya-two, The Old Team has been kicking ass and taking names since before most of The Team was even born. Although they made history, The Old Team is largely forgotten, overshadowed by The Team. The Old Team consists of a few survivors from World War Two, who have usually experienced some sort of time skip to avoid too much aging or are practically unaging, and new heroes inheriting the mantles of the survivors' comrades. They also fight Nazis a lot.
Examples of these organizations in comics: The Justice Society, the Invaders
The Young TeamMembers of The Team have an unfortunate tendency to hoard sidekicks and gain derivative characters much younger than themselves. These youngsters organize into a new team where they don't have to deal with the stuffiness of either The Team or The Old Team. Most members are in the 16-20 age range.
Examples of these organizations in comics: The Teen Titans, the New Warriors
The Government AgencySuperhumans pose a lot of legal questions. Can you use x-ray vision on someone without a warrant? Is anyone who throws on a spandex suit and tries to rob a bank unfit to stand trial?
Stuff like this is the purview of the Government Agency, which is the public face of Human-Superhuman relations.
Examples of these organizations in comics: Department of Metahuman Affairs (pretty sure that's a thing in DC), House Committee on Superhuman Activities
The SECRET Government AgencyWhile the Government Agency is the public face of Human-Superhuman relations, this organization is its private face. At times helpful to Supers and other times harmful, this Agency believes in preparing defenses against a possible Human-Superhuman war and often engages in questionable activities to obtain it.
Examples of these organizations in comics: Cadmus, Checkmate, S.H.I.E.L.D.
The Criminal SyndicateCrime usually pays but in a world with Supers you get diminishing returns.This is where Syndicate steps in. Need some crazy science doohicky? Need some super-powered muscle for a job? The Syndicate is more than happy to provide it as long as you help advance its agenda. From petty crime to global domination, the Syndicate is always hiring!
Examples of these organizations in comics: Intergang, AIM, Hydra
Next, we need to think of people and places. On to Part 2!
Or you can skip to OUTER SPACE if you prefer.