Gilbert Huph, despite being an obvious Hate Sink, is rather popular among fans likely due to Wallace Shawn's over-the-top performance.
Frozone's wife Honey, likely due to her part in one of the best scenes in the film. Not bad for a character we never saw on screen.
Stratogale gets discussed a lot and even has fanworks despite being on-screen for less than ten seconds in the "No Capes" speech. Her being a Kid Heroine who died young combined with the violent nature of her death makes her a frequent source of Tearjerkers.
The Underminer is also well-liked, due to making the absolute most out of his one scene in the movie. The fact that he is the main antagonist of the video game, which was an example of No Problem with Licensed Games, also helps, though his reputation took a slight hit when Incredibles 2revealed him to be nothing more than a simple supervillain bank robber, basically making him the Bomb-Voyage of the 2nd film.
There's also Kari, the babysitter from the "Jack-Jack Attack" short that ended up a Badly Battered Babysitter, likely for the fact that she managed to handle a baby dealing with Power Incontinence without serious injury. She was set to return for a small cameo scene in Incredibles 2 (with her parents even appearing), only for her scene to get cut.
Bomb-Voyage has gained quite a bit of popularity for his gimmick and Gratuitous French dialogue.
Many of the heroes who were listed as fighting the Omnidroids have a decent amount of fan fiction and/or fan art. Some standouts are Blazestone (a Motor MouthBoxed Crook once in a Fire/Ice Duo with Frozone), Macroburst (for being the first to defeat an Omnidroid and their androgynous appearance, along with lacking a gender specification in their NSA file. note It's never made clear if this was a deliberate gender identity statement or an accidental side effect of their wind powers constantly obscuring their voice and altering their hairstyle. Considering that their gender was eventually confirmed to be male in the 2018 Lego Incredibles game, it was likely meant to be the latter.), Hypershock (for his name, costume, and powers), and Stormicide (for some interesting powers, a good design, and some of the humor in her NSA file).
Fountain of Memes: The entire movie has spawned a lot of memes by itself, but Mr. Incredible, Frozone, and Syndrome are the most popular meme targets due to their hammy, over-the-top personalities.
Les Yay: The tie-in comic for Incredibles 2, Secret Identities has Violet become friends with a girl with Sonic powers named Rose and their interactions are filled with this. From their matching names, to the reveal of Rose's abilities and Violet revealing hers being played out like a Coming-Out Story, to the two sneaking out and going out at night together resembling a date, to their incredible closeness at points, to their temporary falling out playing out like a break up because of Rose's father's supervillainy that nearly causes Rose to pull a Face–Heel Turn and almost lands Violet herself in jail due to being an unintentional accomplice in the father-daughter duo's crime spree, which forces Violet to fight Rose herself in the middle of the School Dance in order to save her from her father's bad influence. Even if it's clearly unintentional, it's not difficult to see something in their friendship, especially if one applies the popular interpretation that superheroes are an allegory for LGBT people to the story. Those who have read the comic have argued that Violet ended up having far more chemistry with Rose than she did with her canon love interest, Tony, with some holding out hope that Rose becomes a Canon Immigrant for a potential third film and even potentially hook up with Violet, despite her canon relationship with Tony.note Unfortunately, Rose is highly unlikely to become integrated into the films, given Pixar tends to ignore adaptations made without their involvement (with Incredibles 2 de-canonizing both Rise of the Underminer and the Boom comics)
Moe: All three of the Parr children are downright adorable. Violet for being a Shy, awkward but cute teen girl, Dash for being an energetic and goofy kid who loves pranks and is eager to compete in sports, and Jack-Jack because he is a cheerful baby. They get even more adorable come Incredibles 2 thanks to the 14 years of animation upgrades that further empathizes their cuteness.
Bob struggles to adapt to civilian life and has a corrupt and extremely strict boss in the first film. In the sequel, Bob loses a lot of sleep caring for his children while Elastigirl is crimefighting.
Violet is extremely introverted, being in a family where everyone else is much more vocal, and just wants to fit in with other kids her age. In the sequel, she is emotionally wrecked from the memory wipe of Tony Rydinger, with whom she was supposed to be going on a movie date.
Woobie Family: The Parr family has a hard time adjusting to a world where the use of superpowers is banned. They frequently have to move house, and family life was quite tense until they first fought as a family. In the sequel, the Superhero Relocation Program is shut down, meaning that they would have been homeless had Winston Deavor not offered them refuge. Thankfully, supers are made legal again at the end of the sequel.
Woolseyism: The European French localization translates the "Mr. Incredible" nickname as "Mr. Indestructible" (same meaning in both language), a better description of his superpowers than his original name.