In Suburban Knights, a girl using a cellphone who the villain stumbles upon and kills got quite some attention from the fandom, ever since her one second appearance in the trailer. The director/star even discusses her on the DVD Commentary (she is played by an ex-girlfriend of his).
Sonic the Hedgehog 2: Special Edition. Failure Cresh, one of the series' few original characters, appears in only one level for about five minutes (and later gets a brief mention in the epilogue). In this short time, we learn his entire (hilariously) tragic past and see him (mercifully) die. Consequently, he makes a big impression on audiences.
In the original The Gamers movie, Mark might qualify. Technically, his character is present everywhere the party goes, but he just stands around looking out into the thin air... Except when he shows up late for game-night, in the middle of a losing battle, immediately goes into a Berserker Rage, slaughters all the enemies alone, then leaves because he's got a date. He was literally only doing anything in one scene!
In season 6, Private Jones, played by Gavin Free, who along with having his name pronounced wrong ("Joannes!" "It's pronounced Jones, sir!") is killed off-screen by Caboose in spite of the latter having his hands tied behind his back.
In Season 12, the Federation guard who the Reds and Blues fool by disguising themselves as snowmen.