Asexuality is typically defined as a person who feels no sexual attraction to others. This is not to be confused with aromantic, a different concept that sometimes overlaps with asexuality. Asexuality specifically concerns biological sexual attraction, whereas aromantic concerns romantic relationships. A person can, for instance, be interested in committing to a long-term romance without an interest in sex. Likewise, a person can enjoy sex while being uninterested in romance. Asexuality and aromantic are also spectrums that include several variations, such as demi-sexuality, Grey-A/R, Queerplatonic, and reciprosexuality/recipromantic.
Both concepts are fairly new to mainstream culture, having only really started to gain traction in the 21st century. They are not very well-known compared to other sexual identities such as homosexuality, bisexuality, and heterosexuality. This has led to an unfortunate lack of representation in media of asexual characters. However, the comparatively recent medium of video games has been more open to taking initiative when it comes to representing asexual and aromatic identity.
As these characters are not stated to be asexual or aromantic by their respective games, these picks are by no means conclusive.
5
Control
Granted, the looming XK Class End of the World Scenario presented by the Hiss might be taking priority, but there appears to be very little, if any, sexual or romantic interest among the staff of the Federal Bureau of Control. There are actually several characters in Control who are probably asexual, including some of its leads. Emily Pope, for example, seems way too invested in her science to even think about pursuing any kind of relationship.
But it is worth pointing out that the same is true of player character Jesse Faden. Her biggest connections prior to the game are with her brother and the otherworldly entity she calls "Polaris." She does become close friends with Emily Pope, but this appears to be limited to a professional relationship.
4 Dishonored
Although the original Dishonored focused a lot on interactions between male characters, it did make a noticeable effort to diversify in both its own DLC and the later sequels. That included adding gender, racial, and sexual diversity. But one of the less obvious details was the appearance of an asexual character early on, who was actually a part of the original game. That was Daud, an assassin with an odd storyline, first appearing as a supporting antagonist in Dishonored before becoming playable in its DLC campaign and a major ally in Death of the Outsider. Although he does not have a huge amount of screentime in the original game, he does play a pretty important part: he literally sets the entire story into motion.
Although not explicitly stated in the original game, Daud does show a noticeable lack of interest in most of the people around him. The closest attachment he really has is his organization of assassins, the "whalers" and even they're viewed more like family. Most of the other people in his life who aren't enemies are friends or business partners at best. Daud's asexuality was eventually confirmed by game designer Harvey Smith.
3 Horizon Zero Dawn/Forbidden West
Horizon Zero Dawn and its sequel Forbidden West have gotten a lot of attention for their diverse cast, but a lot of players did not immediately notice one detail about its star. In a medium with an unfortunate history of male bias, strong female protagonists are always welcomed and Aloy did not disappoint. Strong female asexual protagonists are another matter.
For all the relationships she witnesses, both hetero and homosexual, Aloy herself never shows a particularly strong interest in romance of any kind. She seems to have difficulty even connecting with people on a non-romantic or sexual level, and is consistently shown as resisting flirting attempts.
2
The Outer Worlds
Obsidian's The Outer Worlds had a variety of interesting characters, but few resonated with players quite like the socially awkward mechanic Pavarti Holcomb. Her story of a sheltered worker leaving her home colony to explore the greater universe was well-received by fans, but she also got attention for being depicted as asexual.
Although the game lack romance options, getting to know Pavarti reveals some of her long-standing difficulties with meaningful connections and a total disinterest in sex; something which broke up the few romances she did have. Instead, Pavarti has a much closer connection to machines, which she has a habit of personifying. There is even a possible ending Pavarti finds herself preferring the ship's computer for company over human companions.
1 Tomb Raider
Lara Croft has never had much of a romantic life. In fact, across the entire Tomb Raider franchise she has only had one love interest- Terry Sheridan (Gerard Butler) in the movie The Cradle of Life. And she ended up killing him, after only letting him out of prison because she needed his connections. Lara's apparent lack of interest in men has led to some embracing her as an LGBTQ+ icon, and many read her relationship with Sam in the 2013 reboot as homoerotic. One of the writers even admitted to liking the idea of Lara being gay. However, her behavior is a lot more consistent with being asexual.
Lara displays a general lack of romantic interest in anyone. Beyond possibly feeling some attraction to Sam, Lara tends to be better at forming close friendships than romantic ones. She develops a close bond with Jonah by Rise of the Tomb Raider, but it never moves beyond a Platonic status. She is even supportive of Jonah when he becomes romantically involved with a different woman in Shadow of the Tomb Raider. A lot of her strongest friendships are with other women- Sam, Sofia, Unuratu, but she never seemed to have an interest in long-term commitment.