Ace Culture
Here is a non-conclusive list of terminology, symbols, jokes and other such things that are used or were created by the asexual community. Please note: The asexual and aromantic communities used to be united as one in the past. Although they nowadays have more separate identities and spaces, some of the things listed in here are used by both communities.

Terminology aka ace slang
Asexuality: A sexual orientation where a person does not experience sexual attraction; does not feel an innate desire for sexual activity with others.
Ace: Short of "asexual".
Allo, allosexual, zed, zedsexual: Anyone who is not asexual.
Aspec, asexual spectrum: A spectrum that includes any asexual sub-identities. Typically used as a term to refer to asexuals, demisexuals and greysexuals.
Asexy: 1. A synonym for ace (has fallen somewhat out of use); 2. Used to describe something that is attractive in a non-sexual way, things that aces are attracted to (eg. one's baking skills); 3. Used to describe something/someone that is made more attractive by its/their lack of sexuality; 4. Probably even more uses tbh.
Amoeba: Used to refer to an asexual person in the early days of online ace communities (late 90s and early 00s). It's not used anymore.
Demisexuality, demi: An aspec identity, where a person only feels sexual attraction after forming a strong emotional bond with someone.
Greysexuality, grey asexuality, grace, grey-a, grey ace: An aspec identity, where one feels sexual attraction only rarely. A grey area between sexuality and asexuality, hence the name.
Autochorisexual: Someone who may: get aroused by sexual material, consume porn, fantasize or mastrubate, but has no desire to seek a partner or partake in sexual interactions themself.
Apothisexual: Someone who is repulsed by sex.
Libidoist: Someone who has a libido/sex drive.
Nonlibidoist: Someone who does not have a libido/sexdrive.
Of the two aforementioned terms: These words are often used in the sense that a libidoist masturbates, and a nonlibidoist doesn't. That is close to the original use of these words: The Nonlibidoist Society that used to exist separated themselves from asexuals by emphasizing that they do not masturbate. Still, in my humble opinion, "has/doesn't have a libido" is not a very good description in this sense, as nothing is forcing someone with a libido to masturbate, or preventing someone without one from doing so...
Romantic attraction: Feeling a romantic but non-sexual pull towards someone. For most people, their romantic orientation is the same thing as their sexual orientation. For many asexuals, however, making a distinction between the two is useful and an important part of one's identity.
QPR, queer-platonic relationship, quasi-platonic relationship: A non-/ambiguously-romantic relationship that is still "more than just" friends. Partners in such relationships might do things that one wouldn't do with their friends, such as buying a house, living together and adopting children. It differs from the norm of what a romantic relationship is expected to be like.
QPP, queer/quasi-platonic partner, zucchini: One's partner in a queer/quasi-platonic relationship.
Squish: A platonic crush.
AVEN, Asexuality Visibility and Education Network: World's largest asexual organization, founded in 2001. Its goal is to increase the visibility and education on asexuality.
Acephobia: Discrimination, negative attitudes and prejudice of asexuals.

 Jokes and memes
Cake: One of the oldest and best known ace memes. It exists in statements such as: "cake is better than sex" and "make cake, not love".
Garlic bread: Cake 2.0, a much newer meme. One might ask themself: Would I rather have sex or eat garlic bread? If your answer is garlic bread, chances are that you are asexual.
Please help I'm not a meme master.

 Symbols
AVEN triangle, asexual triangle: An upside-down triangle. The straight line at the top symbolizes the spectrum of sexuality: on one end, there is heterosexuality, in the middle bisexuality, and in the other end is homosexuality. The third point at the bottom symbolizes asexuality (in a way it's "outside" of the spectrum). The triangle is often coloured in a white-to-black gradient in a way that the peak that symbolizes asexuality is coloured black. This old symbol has mostly fallen out of use, as it has been replaced by the asexual flag.
Asexual flag: The asexual flag was chosen by voting by asexual communities in 2010. It consists of four horizontal lines, from top to bottom: black, grey, white, and purple. The three uppermost stripes symbolize the same thing as the older "asexual triangle" symbol: the spectrum from sexuality to asexuality. Black is asexuality, grey is the indentities between asexuality and sexuality (demi and grey), and white is sexuality. Purple symbolizes community: asexuals, their partners, and allies.
Black ring: Black ring worn in one's right hand middle finger is a symbol of asexuality. It helps asexuals indentify each other irl. It is important to remember that: 1. Do not assume that everyone who wears a black ring in their right hand middle finger is ace, and 2. Not everyone is out or wants to be public about their asexuality. If you want to ask someone about their ring, you should approach the topic respectfully (such as asking "does your ring have a special meaning?").
Ace of Spades, ♠: An ace symbol. Sometimes a distinction is made so that Ace of Spades = aromantic asexual, and Ace of Hearts (♥) = alloromantic asexual.
Dragons and other fantasy creatures: These are sometimes used as asexual symbols as people say that "asexuals don't exist".
Space: Often part of an "ace aesthetic". Probably because it rhymes with ace. "Space ace" etc.

 In other languages
FINNISH:
Asse, ässä: Short of asexual; ace.