Blame Game

Jack: Wait a minute though, I only stole the gold to get my cow back from you!
Little Red Riding Hood (to the baker): So it's your fault!
Jack: Yes!
Baker: No, it isn't! I'd have kept those beans, but our house was cursed. She made us get a cow to get the curse reversed!

Witch: It's your father's fault that the curse got placed and the place got cursed in the first place!

—Into the Woods

This is when something has Gone Horribly Wrong and it's time to determine who is at fault, but the consequences for this blame can wreck careers and reputations, or even get people killed. Either that or just stubborn pride.

So when someone is blamed, that person tries to pass off the blame to another plausible person, and that person either tries to put the blame back on the first person or pass it to someone else. Essentially the blame is now like a game of "hot potato", hence we call it the Blame Game.

This can happen in comedy as well as drama. In Real Life, a staple of politics, right after any tragedy.

Compare Never My Fault, when someone consistently tries to avoid taking responsibility for his mistakes.

Remember, this isn't just trying to pass off blame once. There has to be at least one return volley.

Examples of Blame Game include:

Film

Mystery Men features a weapon called the "Blamethrower" that makes a couple groups of mooks do this, allowing the heroes to beat them while they're distracted.
A deleted song in Frozen, Life's Too Short, begins with Anna and Elsa's joyous reunion after she flees the court and ends with them bitterly arguing, blaming each other for the rift between them (Elsa accusing Anna of wanting to shut her away and Anna accusing Elsa of shutting her out).

Literature

Four generals at the end of a film version of The Charge of the Light Brigade all try to avoid blame for the order for the charge.
Every time a plan formulated by the Auditors goes wrong, some time is spent on this one. The outcome inevitably goes like this: the plan was a group effort, therefore it's everyone's fault, and if it's everyone's fault, it's no one's fault, because the amount of blame that attaches is as close to nothing as makes no difference. They're very corporate that way.
In The Bible (Genesis 3), God confronts Adam about his having disobeyed his commandment not to eat the Forbidden Fruit. Adam says, "The woman whom you gave to be with me, she gave me fruit from the tree, and I ate," thus passing the blame not only to Eve, but to God. Eve, in turn, says, "The serpent tricked me, and I ate."

Live Action Television

In a recent episode of The Tudors, Cromwell and another lord try to pass off blame for Henry's displeasure with Anne of Cleves.
- Truth in Television, for every single time Henry wasn't happy about something.
A bit of silliness on The Monkees had Mike as a prosecutor accusing witness Mickey of the crime. Mickey promptly confessed, but also incriminated the judge (Peter) ... who admitted his guilt but revealed that Mike was the ringleader.

Mike: I should have kept my big mouth shut!

Music

As Skyclad put it in 'Eirenarch',

Successes have fathers -- but failure's a bastard

Who stole the cookies from the cookie jar?

Theater

The second act of Into the Woods has the songs "Your Fault" (where the protagonists try to name the source of the problem) and part of "Last Midnight" (where the Witch calls the protagonists out on wasting time placing blame rather than solving the problem). It's also a Dark Reprise of the song "Ever After," where everyone had congratulated themselves on their bravery and cleverness to find their Happily Ever After.
The musical Titanic has the ship's captain, owner, and builder singing "The Blame".
Friedrich Schiller's Intrigue And Love ends like this, until the hero's father finally accepts responsibility for his actions.

Tabletop Games

Debriefings in Paranoia, unless you kill everyone else first and perjure yourself on a Biblical scale, without needing to worry about their testimony.

Video Games

Happens with disappointing frequency in MOBA games, where teamwork is essential and no one ever considers that losing may have been their own fault as well. More often than not the losing team will have a flamewar raging among them about who's failed the most which will inevitably be taken to all-chat, much to the annoyance of the winning team.

Western Animation

DuckTales (1987)

Huey: "Whose idea was it to [forget the details]?"
Dewey and Louie: "It was your idea."
Huey: "Whose idea was it to listen to my idea?"

- Then they all run.

Real Life

In a corporate environment, this is called "blamestorming". A recent Direct TV commercial even uses that phrase.
Politicians, political parties, and even countries seem to love to play the Blame Game at each other for all the political problems that they have to face, even if all or even no parties are at fault. Even if it isn't political, the Blame Game can still occur whenever an argument devolves into an argument about who started the original argument. We won't list examples; that would be playing the Blame Game in itself.
Everything associated with the But Not Too Black trope. Especially when concerning the lack of dark skinned models in the fashion industry, or the entertainment industry as a whole. The industry blames the agencies for the lack of hiring, the agencies blame the industry for not booking said models thus causing the agency not to hire them. It becomes a "Chicken Or The Egg" argument.