- A man hitting a woman is scandal, but a woman hitting a man is funny
This is easily the most offensive single trope on the list, especially because it's not confined to the realm of fiction. The more you portray this as okay in fiction, the more it happens in real life, and the more innocent men get physically assaulted and feel like they don't have a right to defend themselves. For real life victims' sake, either have your female characters not be sexists that abuse their one-sided social power in this area (I'm not sure why you would want them to in the first place), or actively flout the double standard by having the male character fight back when it happens.
- Fathers are harsh, mothers are loving
I can already hear you starting to say "But I have statistics here that validate this trope". No, it doesn't matter if it's statistically accurate. Even if trends like this do exist, we have a duty to portray them as false in fiction, because that helps erase double standards - it provides an example of a loving father so that real fathers don't feel like it's somehow natural or right for them to be the strict one and leave compassion to their wives.
Some writers seemingly try to avoid that result by taking it farther and making the dad an outright villain. That might be less actively harmful in the sense that it doesn't glorify bad behavior, but it's even more insulting to real life fathers. I think we've all seen enough of the "strawman chaotic evil sadistic dad" trope.
- The 100% male cast
The most obvious way to be sexist: simply put very few or no women in the story. Look no farther than some of the Assassin's Creed games for a perfect example of this. In the historical past of the games (which is where most of them takes place), the first game has exactly one notable female character, and she is in exactly one scene. Assassin's Creed: Revelations has one female character also, and she is a rescued love interest. Assassins's Creed 3 has exactly one significant female character, and she dies to motivate her son (see below) when she really should have just been the protagonist of the story honestly. Unless you have a specific reason to make an exception, about half the characters should be female.
- The damsel in distress
Of course, the trope that women can't hold their own in the game of fiction and need to be rescued by men all the time. I have some tips on how to do this in a non-sexist way here.
- The all-male family
This one would be funny it wasn't so sexist. A lot of writers don't seem to realize that you can't have a father and sons without a mother. No one ever even asked in the Clone Wars arc that featured this trope (albeit that family had a daughter, still an instance of the trope). Sometimes there's at least a handwave (usually that the mother is dead) but even if so it's still in most cases just an excuse to avoid having female characters in the story: remember that everything in your story that needs to be explained must be so for a reason - otherwise you're wasting time - and so there should be a mother unless there's a good reason not to. If you have a good reason to want only one parent around, remember it's an option to have the father be dead, and it's better to be symmetric by reversing it every other time than to default to the mother being the dead one.
- The female love interest or other supportive character is martyred to motivate the male hero
This happens in Sword Art Online (with Sachi), The Force Unleashed 2, Star Wars: Revege of the Sith (it doesn't literally do what I said but it uses the threat of Padme dying to motivate Anakin and then kills her by complete Death Ex Machina after Anakin turns evil), and in Beneath A Steel Sky, to name some examples. None of these female characters were killed for the sake of their own arcs; on the contrary Padme's arc was ruined for it, Juno (TFU 2) had literally no other role in that story even though she was a major character in the original, and the same can almost be said of Anita (Beneath a Steel Sky).
I (and I believe most men) wouldn't like it if male characters got this treatment as often as women do, so let's not always do it the opposite way. You really shouldn't martyr a character of any gender unless it's the best conclusion to their own arc.
- Asymmetric treatment of nudity
Men are almost never seen naked in fiction. But female nudity is everywhere, whether it's used to take away the character's dignity (as with princess Leia in Episode 6) or to make her sexually attractive to a presumed male and perverted audience (as with queen Ming in Lost Odyssey, or with just about every female character there was in Sword Art Online). In fact, this double standard exists in real life too: men's formal wear covers their entire bodies modestly, whereas women's tends to be very revealing, particularly at weddings.
- 'Lady' is used to talk down to women
For some reason 'lady' is almost a derogatory term in some cases. Consider the following scenario (this is pretty much something that happens in Mass Effect 2 and that the player isn't given a choice to even object to): a woman returns to her house and finds that the police are searching it and there's a guard by the door that won't let her in. She argues with him, but he says, "The law is the law, lady. You can't change it." That sounds natural, doesn't it? But what if the genders are reversed and the guard says, "The law is the law, man. You can't change it." That sounds weird and makes us think, "is there something wrong with being a man?" and rightly so.
- All the combatant men are melee fighters, all the combatant women are archers/mages/medics or other supportive roles
Women are not so much physically weaker than men that they can't ever be fit for a frontline combat role. If you have multiple combatants of both genders and various disciplines of combat in a story or game, you should have at least one female frontline fighter and one male support fighter. Erring on the side of the gender role is fine in this case because this one has some basis in biology, but don't exaggerate reality.
(The reason I consider this trope misogynist and not misandrist is because generally the idea is that women aren't strong/tough enough to be frontline warriors and not that men aren't intelligent enough to be mages or something.)
- Women need help with basic physical tasks
I really hate to say it, but Doki Doki Literature Club is going to have to be my example here. In an optional scene, the following excerpt takes place:
"Sayori hastily bends down to pick up the piece she dropped."
"But being inattentive of her surroundings, she bumps right into me."
MC: "It's fine, it's fine."
MC: "I'll get it for you."
"I bend down and pick up the broken pencil."
"Sayori clutches the desk beside her to support herself, knees shaking."
Sayori: "I-I'm a little clumsy today..."
MC: "Let's sit down, Sayori..."
"I grab Sayori's arm and help her sit at the desk."
I get that Sayori is clumsy. But does she really need help with picking up a pencil and sitting down? I knew a 1-year-old who could do those activities on her own.
- Men are just, women are kind
This is distinct from the misandrist trope that fathers are harsh and mothers are loving, because there the implication is that one is good and the other is bad while here the implication is that both are good, they just specialize in different virtues. And there's nothing wrong with that in a vacuum, it's just that it's become such a cliche that it's kind of just assumed, both in fiction and in real life. We could use some stories that invert the stereotypes to remind us that this isn't built in to human nature.