Though it is just a joke form in the SMG4 series, many characters had managed to achieve said transformation.
The Super Saiyan form's first appearance was in R64: Mario Simulator. The superior form of Super Saiyan, Super Saiyan 3, made its first appearance in SMG4: Mario VS Steve at the end of the video. The Super Saiyan 2 form was skipped.
UsersShigeru Miyamoto appears on the screen and complains angrily, Mario loses his temper and throws the Nintendo 64 and the cartridge out the window, flies to them and starts farting and pooping fire on both of them. He then starts yelling and flexing before he turns Super Saiyan. He flies into outer space and throws the cartridge into the Sun, where on impact, it explodes, destroying everything and everyone in the cartridge. Mario then says his so far only quote, "I did it! I saved the world!" But he doesn't notice that the Earth then explodes after that.
Super Saiyan Mario can be noticed in a DeviantArt art picture at the end of SM64: ṩṩἔᾗмὄḋᾗᾄʀ 7 (TOAST edition) and made a reappearance in Mario vs Pokemon GO where he briefly turns Super Saiyan and captures the entire Earth with a Pokeball.
In SMG4: War Of The Fat Italians 2019, during an arm-wrestling challenge, both Mario and SMG4 achieved the Super Saiyan 3 form due to the intensity. Though Mario proved to be stronger, his arm was ripped off due to strain from his enormous power, making him lose.
Additionally, in SSENMODNAR DELUXE - 1 MILLION SUB SPECIAL, when SMG4 is celebrating achieving 1 million subscribers, a Thwomp with Super Saiyan hair is briefly seen.
When Steve cornered Mario and threatened to kill him unless he admitted Minecraft was a good game, Mario lied that it was and rubbed it on Steve's face. Furious, Steve transformed into a Super Saiyan 3 and used its power to overwhelm Mario and nearly kill him.SMG4: Mario and the Anime Challenge during a challenge where he, Mario, and Fishy Boopkins must scream as loud as they can. Upon winning the challenge, Bob transformed into that form and claimed himself to be almighty. However, when Ultra Instinct Shaggy (from the meme of the same name) heard that, Bob, knowing how powerful he was, depowered quickly.
Goku from the Dragon Ball franchise is obviously capable of going Super Saiyan (being the one who started the thing), having transformed upon seeing the death of his best friend at the hands of a certain tyrant.
When Francis summoned Goku with the Inkweaver, the latter was in his Super Saiyan God form (actually his Super Saiyan Blue form which is superior) and ordered him to kill SMG4's gang when they refused to leave without Meggy Spletzer, whom Francis had kidnapped. True to Francis' word that he was "the most powerful anime character", Goku easily dispatched the gang, even blocking Luigi's powerful Green Missile Attack, and was about to kill Tari, until Axol took the Inkweaver back from Francis. While Tari distracted the mighty Saiyan (by challenging him to a battle of Dragon Ball FighterZ), Axol summoned Ultra Instinct Shaggy (from the meme of the same name) and Goku, after losing the match and destroying the ink tank containing Meggy, fought him, while the battered Mario desperately tried to find Meggy in the rubble. UI Shaggy easily subdued Goku, forcing him to self-destruct as a last resort. While UI Shaggy succeeded in getting everyone including the now-humanized Meggy off the island, Goku exploded, destroying Anime Island and everyone in it.