Hmm, characters who didn't add anything.
Classic example is Big. He didn't add anything at all. It would've been forgivable if he hadn't had the personality of a particularly benevolent troll. (I'm referring to the type that lives under a bridge, not the internet type, though that type may also live under a bridge.) I actually have a mostly merciful outlook on the rest of the cast, though Shadow probably shouldn't have been resurrected as it ruins the impact of his sacrifice at the end of SA2, though some would argue it was a case of "back by popular demand" as opposed to just plain lack of imagination on the part of Sonic Team, though I'm more inclined to believe it was also a bit of executive meddling.
I can't really think of any other serious examples... yeah, characters like the guild master are annoying but thats more a case of bad character design than being genuinely useless. I suppose the hero could've by-passed him completely and just had Maze training him, but then it would've just been Maze's annoying voice in your head instead of the guildmasters (Until a certain point in the story of course.)