The Kunai is a recurring weapon in the Street Fighter series. It has been used only by ninja characters such as Guy and Ibuki.
Users
Ibuki

As the Kunai is Ibuki's signiture weapon, she often uses it in battle and even outside such as winposing and outfit aesthetics.
The Kunai in Street Fighter is most commonly associated with Ibuki. Somewhat ironically though despite her high association with the weapon she only had one Special Attack attack dedicated to it and one Super Art that utilized the weapon in Yami Shigure. Instead, her association was mostly established with posing with the weapon during some midround transitions, introductions and winposes. Though later Ibuki started getting to use her Kunai more, usually through in game-specific attacks such as her Focus Attack in Street Fighter IV and she hits her opponent with a Kunai in Street Fighter X Tekken with her Launcher.
Street Fighter V changed Ibuki's moveset to be more weapon focused thus increasing her reliance on the Kunai (though ironically also gaining a character unique limited count system in the process). Increasing her Kunai attack's utility with a new ground-based attack (which isn't unlike Geki's ability to throw shurikens) and very different properties when using EX meter. Also gaining a throw system with Kunai Ikkinage where she throws all her remaining Kunai to maximize damage and Kunai Hoju to refil said used Kunai.

Kunai themed clothing accessories.
Furthermore, with alternate costumes, Ibuki commonly gets Kunai aesthetics, for example with her second IV alternate she has a chain of kunai around her jeans. In her Sporty V outfit on her clothes, she has Kunai printed at her hips and at the back of her top. In her hidden Nostalgia outfit, Ibuki's default top is removed and kunais she usually keeps hidden near her chest is shown.
Guy
Guy was seen to keep Kunai with him during his ending in Super Street Fighter IV. He used them as an intimidation weapon when M. Bison was carrying an unconscious Rose in his arms. Guy was never shown using the weapon however and his true proficiency with the weapon isn't known. In game he uses hand to hand combat and doesn't take out weapons even during his winposes. It should be noted that while in the original Final Fight while all playable characters were associated with a weapon Guy's was not a Kunai.
Unknown User
During Fei Long's original Street Fighter IV ending after Seth ends his speech he suddenly falls to the floor. On his back, a Kunai is shown to have taken him out. It is not known who threw this Kunai, as the camera never shows who did it and Fei Long was in front of Seth the whole time, so he never would have had the chance to strike the area. Ibuki isn't a probable candidate as she is rarely part of the main plot of games (and wasn't in this version) and it is commonly speculated to be Guy (though this has never been proven nor denied).
Trivia
- The logo for Super Gem Fighter Mini Mix added a Kunai to the logo (specifically to hold the "mini mix" portion). As the logo for both Gem and it's Japanese version Pocket Fighter have each character represented the Kunai in Gem Fighter represents Ibuki.
- This also means Ibuki had no representation in the Pocket Fighter logo, as no Kunai appear in it.
- Coincidentally Guy also appears in this game through Ibuki's ending. Making both of SF's Kunai users represented to a capacity.
- This also means Ibuki had no representation in the Pocket Fighter logo, as no Kunai appear in it.
- In-Game the regular Kunai has been one of the lowest damage weapons, doing just 30 in Street Fighter X Tekken for example.
- Neco Drop's description for Ms. Donka references the kunai weapon.
- In cutscenes and comics where Ibuki uses her Kunai it usually instantly kills her target. In game the Kunai does among the lowest damage out of any attack in the game.