"Most of what is unusual about man can be summed up in one word: 'culture'. I use the word not in its snobbish sense, but as a scientist uses it. Cultural transmission is analogous to genetic transmission in that, although basically conservative, it can give rise to a form of evolution."—Richard Dawkins, The Selfish Gene, Chapter 11
Sociology notwithstanding, on the Internet, a "meme" (pronounced "meem") is usually described as a catchy derivative of some aspect of pop culture, parodied and repeated to the point that its origins and original meaning become muddled and completely mutilated beyond any point of recognition or humor. It can even be Wrongfully Attributed.
Which means we don't want them in All The Tropes articles, because we are not interested in being muddled, dated, and beyond humor.
Fandom being what it is, this also applies to characters. The Internet is liable to spread a "meme" version of a character which is totally (sometimes deliberately) at odds with the original depiction, such as a cheerful version of a dark or scary character, a sexy version of a character featured in a Jekyll and Hyde episode, or softening a depressed one into a simply unlucky character.
Another quirk of memes depends on where they're initially propagated. Memes often spread regardless of content, taste, or sensibilities, while the original source may be the only ones who know enough about the source material to use it ironically. As well, some memes reference something common, but become catchy enough to be associated with only a single new thing.
Depending on how strongly the production company is tied with Fandom, sometimes a meme can escape the internet and get referenced in the medium it parodied through Bonus Material or Popularity Power. When this is the case you get an Ascended Meme. Some forgotten or Discredited Memes are even resurrected thanks to the Popularity Polynomial.
Note that while this article refers to Internet-based memes, the phenomenon is not just limited to the Internet. It can be Sein Language which is that unique blend of terms you and your friends use, or a simple Catch Phrase that is repeated over a billion times. However, certain memes are only popular to a certain group.
For in-universe examples, see Instant Web Hit.
If you'd like to keep up with the memes of the day, go to Oh Internet or Know Your Meme, or The LURKMORE Wiki (NSFW), or the fine folks at Encyclopedia Dramatica (Even more NSFW). These are all examples of great resources for the memes themselves and the enigmatic culture around them, but beware the interstitials. You Have Been Warned. On the other hand, if you just want to learn who starts many of these, see Fountain of Memes. These are probably the most common source of Surreal Humor.
The Trope Namer (for the word meme) is Richard Dawkins, who suggested a Mind Virus-like model of society: that cultural information is inherited and reproduced, occasionally with minor mutations, in a similar way to genetic information.
When adding to one of the subpages, please write the meme, then add the explanation of the meme inside a footnote titled "Explanation." 
Sub-Tropes and specific variants (add new examples to those pages, not here):
- Live Action TV
- Other Internet
- Professional Wrestling
- Tabletop Games
- TV Tropes
- Video Games
- Web Comics
- Real Life
- Ascended Meme
- Beam Me Up, Scotty (with quotes)
- Candle Jack
- Caramelldansen Vid
- Chuck Norris Facts
- Fauxtivational Poster
- Forced Meme
- Fountain of Memes
- Image Macro
- In Soviet Russia, Trope Mocks You
- Inspector Spacetime
- Instant Humiliation - Just Add YouTube
- Interrupting Meme
- The Man Your Man Could Smell Like
- Memetic Badass
- Memetic Bystander
- Memetic Hair
- Memetic Molester
- Memetic Outfit
- Memetic Sex God
- My Little Pony: Friendship Is Magic
- No, You
- Pothole Magnet
- Red Zone Remix Vid
- "Ruby", as played by an Angry Marine
- Sein Language
- Stay in the Kitchen
- Step Three: Profit
- Stupid Statement Dance Mix
- There Are No Girls on the Internet
- Tropes Will Ruin Your Life
- The Ugly Barnacle
- Voice Clip Song
- Verbal Tic
- Watch It for the Meme
- Wrongfully Attributed
- YouTube Poop
- This is just the example. Follow it this way.