Sexism is a real issue in the real world. However, the seemingly endless allegations of sexism in gaming undermines the struggle against it somewhat by making the cause appear more focused on shallow victories than actually addressing the root causes and trying to fix it. That's not to say that there's absolutely no sexism in games, of course—2013's Remember Me had many prospective publishers back out solely because the main character was a woman, and let's not even get into the existence of bikini armor. However, always missing from the debate and its alternating bile and white-knighting is the other side that highlights strong female roles dating back all the way to gaming's early days.
Chrono Trigger (1995)
Not only is Chrono Trigger one of the best Super Nintendo games ever made, but it's still considered by many of its fans to be one of the greatest games ever made. In it, you play as Crono (minus the H), an orange-haired kid with weird friends and a habit of getting into trouble. Over the course of his journey, he finds allies in unlikely places with whom he joins forces, time-traveling to and from key time periods in order to stop the world from coming to ruin. More relevant to the topic at hand, Crono's allies include the tomboyish princess Marle, the warrior chief Ayla, and the brilliant inventor Lucca. At no point are any of these female characters depicted as being lesser than their male counterparts, and Ayla in particular is even shown to boss around subordinate Kino (a male), as well as being uniquely capable of performing a critical hit that does 9,999 damage. To put that into perspective, 9,999 is literally the most damage a single character can inflict in a single attack, and none of the other characters can even come close when leveled up to their max levels and equipped with their best weapons.
Planescape: Torment (1999)
Much like Chrono Trigger, the story-heavy Planescape: Torment is considered by its fans to be one of the best games ever made. Developed using the Infinity Engine popularized by games such as Baldur's Gate, Torment casts you as a heavily-scarred amnesiac with tattoos on his back and an inability to die. As The Nameless One (TNO) makes his way through the game to discover answers about who he is and why he's unable to perish, he joins up with some of the most memorable characters in all of gaming, from talking skull Morte to chaste succubus Fall-From-Grace. Again, none of these female companions are ever shown to be any less capable than their male counterparts, with Annah and Fall-From-Grace possessing a level of street smarts that few other characters apart from Morte demonstrate.
Planescape is also an interesting example because of the non-playable character of Deionarra, a female ghost who claims to know TNO. She's also madly in love with him to a distressing degree, and this inevitably leads to a stunning piece of dialogue that reveals the nature of TNO's character in a previous, unremembered life. This raises two intriguing questions: is it sexist to portray a certain gender in a more submissive light if it's done for narrative reasons, and if so, is the answer to include an equally submissive male character for the sake of parity? Certainly the game would have suffered greatly had her character not been present, and it's likely that shoehorning in an unnecessary male character to avoid allegations of unfair treatment would have been a mess (as superfluous characters very often are).
Max Payne 1 (2001) & Max Payne 2 (2003)
Mona Sax is one of the greatest game heroines ever created. Not only is she a hired killer who has a brief stint as a playable character in the second game (whereas the first game only features her in some of the cutscenes), but she also saves main character Max on multiple occasions and survives a bullet wound to the head. Chuck Norris and a pre-demise Bruce Lee could merge together into a super being to oppose her and the smart money would still be on her walking away unscathed.
Velvet Assassin (2009)
Violette Summer, the main character in World War 2 stealth game Velvet Assassin, is loosely based on real-life WW2 spy Violette Szabo. This is another interesting female portrayal, because while she's shown to be incredibly capable over the course of the game, those looking to prove that games are sexist will likely focus on the fact that she can enter a "morphine mode" where she freezes time and runs around in a nightgown. What that would completely ignore is that there's nothing remotely sexual about it, the mechanic instead tying into the fact that she's recalling previous missions while dreaming in a hospital after being injured in one of said missions. The morphine, then, is her "present self" being injected with morphine and bleeding into her memories, and she's in a nightgown in the hospital. At the end of the day, hers is one of the stronger, more realistic female portrayals in recent years.
Murdered: Soul Suspect (2014)
Finally, Murdered: Soul Suspect, a game that released in 2014. In it, you play as Detective Ronan O'Connor, a police officer who dies off faster than a redshirt in Star Trek and has to then solve the mystery of his own death. His only means of doing so comes in the form of Joy, a headstrong teen medium who's reluctant to help and who has a tendency to oppose authority at every opportunity (even attempting to break into the police department alone at one point). While Ronan may be the playable character, it's only thanks to Joy's contributions that Ronan is able to solve the case of the Bell Killer, and she ultimately proves to be every bit as much of a main character as he is.
These aren't cherry picked examples. Here are several more female characters in games that are every bit as deserving of paragraphs detailing their strengths: April in The Longest Journey, Rose in Legend of Dragoon, Kepri and Yenna in Tales of Illyria: Beyond the Iron Wall, Nilin in Remember Me, Samantha in Gray Matter, Alejandra in Papo & Yo, Billie in the Dishonored: The Knife of Dunwall DLC, Scarlett and Catherine in Divinity: Dragon Commander, SIE in Alpha Protocol, Raynie in Radiant Historia, Scarlett in Venetica, Emma in Front Mission 3, Layl in Sword of Hope 2, Selan in Lufia 2, Feena in Grandia, Meryl in Metal Gear Solid, Kid in Chrono Cross, Cate Archer in No One Lives Forever, and countless others spanning just about every gaming platform in existence.
Are video games sexist, then? Yes and no; the industry itself has a bit of a sexist streak in its reluctance to trust new intellectual properties to female main characters, which is no doubt why the industry is flooded with so few games that cast women as the main characters. However, the games themselves often prove to be decidedly not sexist. The argument over whether this-and-that new game is sexist, then, is ultimately a roundabout one that only serves to slowly undermine the very real problems women face with discrimination, the gender pay gap, and a number of other issues. Better debates to have about female roles in gaming would be over why publishers believe that games with female main characters aren't a safe bet to back, as well as questioning whether the games that portray females as bikini-armor-clad supermodels and males as He-Man impersonators are actually catering to any real demographic's tastes, or if they're pandering to an imagined group of gamers.
Seeing sexism in everything is kind of like having a lucky number: it's not long before you begin to see it everywhere. After all, when you're alerted to something, you're far more likely to ignore all of the times you don't see it and focus solely on the rarer times that you do see it. It's better to start a debate that could actually serve to change people's minds and create movement toward a more inclusive gaming future than to nitpick the smaller details and force both sides into extremes. Nothing short of the former will actually cause anything to change.