Meta Knight himself is also one, starting as just another boss in Kirby's Adventure, then became the focus of one of Super Star's games, then becoming a plot-important character in some games like The Amazing Mirror and Squeak Squad, became a playable character in Super Smash Bros. Brawl and returned in the next Smash Bros. game, and then became one of the playable characters in Return to Dream Land. He's absent from Triple Deluxe, for some reason. ( Although his dark counterpart returns as the final boss of Dededetour.)
Many of the enemies may also qualify, such as Waddle Doo and Knuckle Joe (who might both owe this to the anime).
The one-shot characters from Kirby 64, such as Adeleine, Ribbon, and 02 have a TON of fanart for them. 02 may mainly have been popular due to being suprisingly symbolic for a Kirby game (he spits out blood) and due to his Crowning Music of Awesome. 02 even got a remix of his theme music in Brawl. Ribbon's popularity is probably due to her implied relationship with Kirby. Adeleine became a recurring character in the webcomic Brawl in the Family.
Bandana Dee, who went from one-shot opponent in a Super Star minigame, to the confirmed identity of the Waddle Dee boss in the remake (with speaking parts!), to a playable character in Kirby's Return to Dream Land, is gaining in popularity lately. Some Fanon even holds that he's the same Waddle Dee who partnered with Kirby in Kirby 64, just without his Iconic Item.
He's even become a very popular request for Super Smash Bros., and given how important he is nowadays, it's easy to see why some people thought he might have been a candidate to be put in.
Kirby 64 is a Darkhorse game for the series. Aside from starring the aforementioned characters, it's a great aversion of Polygon Ceiling, opting for a 2.5D presentation that keeps the gameplay unchanged, while providing some of the best animations and background art for the console. It possesses a fair amount of challenge while not being unfairly hard, and the popular mechanic of combining powers hasn't been seen since. Nowadays any game featuring character cameos or remixed music from the game is typically met with enthusiasm by fans.