Abandon Shipping: Ethan/Brandt, which was once one of the popular ships in the fandom behind Ethan/Benji, gradually dropped in popularity when Brandt didn't appear in Fallout due to his actor Jeremy Renner having scheduling conflicts with Avengers: Endgame and the low chance that he'd appear in any future installments, with many Ethan/Brandt shippers gravitating to Ethan/Benji instead.
Complete Monster: Ethan Hunt and company have faced numerous terrorists and other criminals. Owen Davian and Soloman Lane, however, are the worst of the worst.
In the third film, Owen Davian is a sociopathic, powerful international Arms Dealer who is notorious for selling to different terrorists. Davian wants to find the Rabbit's Foot, a highly dangerous weapon which Davian is going to give to John Musgrave and start a war in the Middle East which would kill many people. When he captures an agent who is spying on him, he brutally tortures her and plants a bomb inside of her head, detonating the bomb when she is finally rescued. When Davian is interrogated by Ethan Hunt, he gloats about killing the agent, saying that the only real reason he did it was because it was fun, before threatening to do the same to Ethan and his wife, no matter what, which he attempts to do multiple times, even going as far as to disguise his own security chief as Ethan's wife, and then killing her, just to torture Ethan. In his final moments, he keeps his promise, and decides to kill Ethan's wife, with Ethan Forced to Watch.
In Rogue Nation, Solomon Lane is a former MI6 operative who, after realizing his own sociopathic nature, became enraged and went rogue with the Syndicate to cover up his own deficiencies. Using the Syndicate to carry out devastating terrorist attacks while committing murders himself, Lane was defeated and arrested by Ethan Hunt and his team. Two years later in Fallout, Lane uses his ally John Lark—aka August Walker—to get free, now hell-bent on revenge against Ethan. To that end, he uses stolen plutonium to rig two nuclear bombs to go off in Kashmir, at a medical site where Ethan's ex-wife Julia is working just out of spite. The nukes will irradiate the water supplies of China, India and Pakistan, affecting a third of the Earth's population while Lane is fine dying in the blast so long as he knows Ethan is framed for being Lark and will rot in a jail cell for the rest of his life haunted by the guilt of Julia's death. Abandoning all pretense of good intentions, Lane shows that he is a dark mirror to Hunt himself, stopping at nothing to achieve his ends, no matter how many have to die.
Fandom Rivalry: There are passionate arguments between M:I fans and James Bond fans about which is the best Spy Fiction film series of the current era, more exactly between the M:I movies since Mission: Impossible III and Daniel Craig's Bond films.
Fanon Discontinuity: Fans of the original series like to pretend the films never existed mainly due to Phelps turning out to be a villain and Tom Cruise stealing the spotlight.
Ethan Hunt/Benji Dunn aka Benthan is the biggest ship in the fan base. This is mainly due to the chemistry between Tom Cruise and Simon Pegg and the Ho Yay that they have in later films. On most sites like Tumblr or AO3, Ethan/Benji easily outranks Ethan being shipped with either his former wife Julia Meade or his new canon Love Interest Ilsa Faust.
Julia was married to Ethan before eventually getting remarried to Erik. Despite this, pairing Ethan and Julia also remains very popular among fans today, mainly because Erik has very little characterization beyond being a Nice Guy.
Even Better Sequel: An unusual case where each film has (bar John Woo's entry, see below) received better critical reviews than the last one, with many now calling Fallout the best installment. The Rotten Tomatoes ratings for all six are, from one to six: 63%, 57%, 70%, 93%, 93% and 97%, while the Metacritic scores are: 59, 59, 66, 73, 75, and 86.
Memetic Badass: Ethan Hunt (and/or Tom Cruise himself). He almost doesn't need any additional elevation given the death-defying stunts he has to pull in every instalment, but he's nevertheless elevated to near-immortal status in the public consciousness.
My Real Daddy: J. J. Abrams, who directed and wrote the third film and has remained onboard the series as producer for all subsequent installments, and Christopher McQuarrie, who contributed to the fourth film and wrote and directed the fifth and sixth. Under their involvement, the films have been seen blending a strong mix of the more cerebral mind game aspects of the original movie and the more over-the-top action set pieces of the second, as well as introducing mainstays in the series like Benji Dunn and Ilsa Faust, with the more consistent cast allowing a greater focus on the whole team ensemble that some detractors of the first two films felt were missing. Since the two have gotten involved the series has been getting better reviews with each film, with the sixth getting the strongest yet. This also extends to Ethan's characterization in the movies beginning with M:I 3, combining his personality as The Chessmaster who outsmarted his enemies and never fired a gun or threw a punch in the first movie, with his gun-toting action hero portrayal in the second, and having them complement each other, so that while he is adept in a fight and can hold his own well, he primarily prefers out-thinking his opponents and only relies on direct combat if he's left with no other recourse. It's this characterization that stuck, and has continued through all the sequels after the third.
Sophomore Slump: While some moviegoers appreciated the easier-to-follow storyline, Mission: Impossible II is considered inferior despite (or because of) the flashy action (noticeably, it gets the smallest real estate on the six-film collection box art seen on the main page). The third film was seen as much better and getting things back on track. The fourth, fifth and sixth are the best reviewed films in the series.