Especially memorable as the three characters who are not Doris are all ANGELS. The one who explicitly admits to being scared of her, and that Doris has far worse in store for the girl (Lucifer's niece), is an Angel of Vengeance.
In A Very Potter Musical, Molly Weasley and Rumbleroar are each in only one scene, but no one is likely to forget either of them.
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.
Bob and George has Random, a Ran recolor. He is introduced and killed off (in the same way that Ran frequently is) in the span of two strips, except unlike Ran, his death sticks.
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.
The rare serious case is Season 10's Sigma, who appears in only a few scenes but is a memorable and terrifying villain.
In Season 12, the Federation guard who the Reds and Blues fool by disguising themselves as snowmen.
RWBY has some badass characters who die shortly after being introduced, but caused a great impression. These include Tukson the bookstore owner in Volume 2, an airship pilot voiced by Travis Willingham in Volume 3, another airship pilot ("Pilot Boi") in Volume 5, White Fang leader Sienna Khan in Volume 5 (who was even brought back for a supporting role in a short), and Tock the crocodile Faunus in Volume 6. Team FNKI, while they don't die, are also vastly more popular than their half-episode role in the series would suggest.