First things first, the SEGA continuity:
Classic Era: Sonic, Sally, Nack, Honey, Tiara, Knuckles, Espio, Bunnie, Tails, Amy, Mecha Sonic
Honorary mentions to Vector, Mighty, Rocket Metal, Witchcart, Tails Doll, Rotor, the Kukkus, and the SSSSS Squad.
Dreamcast Era: Tikal, Shadow, Rouge, Omega, Blaze, Silver, Mephiles
Honorary Mentions to Biolizard, Iblis, Black Doom, Cream, Chaos, Emerel, Gemerel, and Lumina
Modern Era: Most of the characters introduced here were lame. If i had to choose one, it would be either Marine or Shade. Pickle is a runner-up too.
Lost Mind: Zeena is the one I least hate, though they all suck.
Now for the animated series:
AoSTH: Breezie, Roxy, Katella
Honorary mentions to Mama Robotnik, Wes Weasely, Sonette, and Miss Possum
SatAM: Lupe, Nagus, Snively, Antoine
Underground: Sonia and Manic, Mindy LaTour
X: Cosmo
Honorary mentions to Molly, Topaz, and Bokkukun
Boom: Sticks and Perci
And now the comics
Early Archie: None, really. All of the pre-Penders characters sucked. Well, I guess i'd pick Larry as my favorite if he counts. I kinda liked the one-shot character Botman.
Early Penders Era: Julie-Su (though I used to hate her when I was a Knouge nut), Geoffrey St. John, Lien-Da
Honorary mention to EVE
Middle Penders Era: Mina Mongoose, Dimitri, Leeta and Lyco, Rob O' The Hedge
Honorary Mentions to the Iron Queen, Elias and Megan Acorn, and Monkey Khan. Oh, and Saleta and Sally-Zilla.
Late Penders Era: Fiona Fox, Lara-Su, Dr. Finitevus
Flynn Era: Scourge, Shard, Alicia, Buns
Full SEGA Mandates Era: Eclipse, Relic, Cassia, Clove
Honorary mentions to Coral and Pearly.
Early Fleetway: Megatox (IMO the most frightening Sonic character ever created.)
Honorary mentions to Johnny and Porker (duh)
Middle Fleetway: Tekno, Shortfuse, Morain, Ebony, Brutus, Emperor Metallix, Dr. Zachary
Late Fleetway: Death-Trap
STC-O (If it counts): Vichama
Can't really say for the OVA, Martin Adams books, or anything really obscure.