The Alleged Boss

Cam: I've ... really enjoyed working for you, Dr. Brennan.
Brennan: In fact, Dr. Saroyan, I worked for you.
Cam: We both know better.

—Bones

Maybe he is hopelessly incompetent. Maybe he was set up as a leader in early episodes, but Characterization Marches On. Maybe he's an Obstructive Bureaucrat that presides over a band of Bunny Ears Lawyers who've long ago seized control. Maybe his second in command is Hypercompetent Sidekick, and has been pulling the strings for years. Regardless of the reason, this trope is about bosses who just don't act like bosses.

There are four main types:

A boss who is so incompetent and clueless that he does not even realize that he has no real power.
A boss who does not act like one (e.g., wants to be best buds with the employees) but still has real power in the company and should not be directly disobeyed or offended.
A boss who acts like a 'proper boss' but actually lacks the power to make the employees always obey him. Often the problem is caused by a few Bunny Ears Lawyer types whom he simply cannot afford to fire.
A positive version: a boss who exchanges power and control for the friendship of trusted "subordinates", usually as part of workplace True Companions.

Any Obstructive Bureaucrat or Reasonable Authority Figure is very prone to this.

Any Bunny Ears Lawyer, Hypercompetent Sidekick, Cowboy Cop or Almighty Janitor is very prone to causing this.

Nothing to do with video game Bosses.

Examples of The Alleged Boss include:

Anime

Misato in Neon Genesis Evangelion is qualified. Her orders come off as more motherly than bossy, and she acts like a sister at home.

Literature

This is a major theme in Atlas Shrugged/ Alleged Bosses are among the book's prime villains, and they are villains precisely because they fail to act like bosses. Case in point: Jim Taggart, who is the president of a large railroad company but is so spineless and incompetent that it's his sister Dagny, the company's Vice President, who actually runs things.

Live Action Television

Ron Swanson from Parks and Recreation is technically the head of the Pawnee Parks Department, but as he wants nothing to do with government, he delegates all his duties to Leslie. Unlike similar examples, he doesn't get too chummy with the other employees.
Bones: Cam may struggle--and occasionally succeed--at maintaining her authority, but it doesn't always work. Generally Type 4 or 2.
Beckett is a Type 3 or 4, from Castle. Her team loves her, but doesn't always obey her orders. Summed up when Ryan and Esposito pull a risky and illegal stunt and are surprised when she chews them out.

Ryan: Wow, you actually sound like our boss.
Beckett: Just tell me ahead of time next time so I can help!

Who runs NCIS again? Morrow, Shepard, and Vance, or Gibbs? Hint: he can only be killed by silver bullets. Maybe. Type 3.
On NCIS: Los Angeles Heddy is firmly in charge of the LA office and the agents know that she will punish them if they get out of line. However, the feeling among some NCIS higher-ups is that she over steps her authority and treats her superiors as Alleged Bosses (similar to Gibbs). On a smaller note Cullen is the senior agent-in-charge and technically the boss of the other agents on his team but while he is the leader, he lets Heddy handle all the boss duties.
In Plain Sight: Stan thinks he's in charge. He really does. He's slowly graduating from Type 3 and 4.
Type 2. Station owner Jimmy James in News Radio. While he occasionally comes down for serious business, most of the time he just hangs around and shoots the breeze.
The Office US: David Brent qualifies. Also, Michael, Andy . . . the show seems fond of this trope.
Jack of Just Shoot Me.
On Leverage the team go after a standard Corrupt Corporate Executive target, a CEO embezzling from his company. However, once they infiltrate the company they discover that the guy is incompetent and so overwhelmed by his responsibilities that he has no control over what is happening in the company. He is a former football star who inherited the company and the position. The team now has to discover which of the employees is manipulating the company from behind the scenes and setting up the CEO as a patsy. Later subverted when it's explained he's a decent executive . . . when everything is explained in football metaphors.
The Closer: Brenda pretty much gets her way, regardless of Chief Pope's opinions. Occasionally subverted, but usually not.
Type 4. Within the West Wing True Companions, hierarchy and rank tend to get blurred.

C.J.: I'm assigning an intern from the press office to that web site. They're going to check it every night before they go home. If they discover you've been there, I'm going to shove a motherboard so far up your ass...What?

Josh: Well... technically, I outrank you.

C.J.: So far up your ass!

Han from Two Broke Girls, who gets no respect from any of his employees. They also get away with a lot, including being rude to nasty customers--which is entertaining and funny, but likely to get you fired under a good boss.
Col. Henry Blake from M*A*S*H was supposed to be in charge of the 4077th but outside of the Operating Room most of his time was spent boozing, recreating, or philandering. His Hypercompetent Sidekick was well understood to be the person actually running the camp. Also the dueling doctor factions who were supposed to be Henrys subordinates were frequently overstepping or walking all over him in order to carry out their zany schemes. Blakes replacement, Col. Potter, was able to command a lot more respect and thus appear more in charge.
House: Type 3. Even though Cuddy is the one in charge, House tends to walk all over her to get what he wants. She is still an incredibly competent boss, however, and is usually able to stop him from going too far.
The chain store the main cast of Between Failures works at goes through managers so quickly that none of them ever get the chance to be real bosses, letting Thomas effectively run the whole store the way he wants to.
A mild example is Colonel Mitchell in the last two seasons of Stargate SG-1. While he's nominally the team leader, as he points out to General Landry Daniel and Teal'c are civilians and Carter's the same rank as him, while he's the new guy on a team of living legends, so getting them to do something they don't want to is a little tricky. Type 4.

Tabletop Games

Warhammer 40,000: Orks think humans employ this trope, as there is no easy way (for orks, the leader is automatically the biggest ork, an humans are all the same size to them, or led by smaller men) to tell one from another save their clothes.

Video Games

Squall from Final Fantasy VIII is an easy qualifier due to his age. Everyone wants him to be the leader, but if he started being as jerk of a boss as he (supposedly) is as a person, the team would probably just comment that the much never Quistis is actually older than him, and higher ranked.

Western Animation

Rebecca Cunningham of Tale Spin plays with this. She has Control Freak issues and is perfectly willing to push Baloo and others around in her schemes; however, she is usually all bark and no bite, and usually acts more as a bossy childish friend than an authority figure, something Baloo takes advantage of time and time again.
In The Simpsons Karl is apparently Homer's supervisor. He mentions this only once to get him to stop insulting him and for the rest of the series acts as Homer's drinking buddy and even joins in on some of his antics.

Real Life

Acting like this in real life (as a wimpy boss or insubordinate employees) is an excellent way to get fired. There are some places where hierarchy gets blurred, but you have to be careful.