Even for a computer AI designed to assist you, Cortana goes above and beyond the call of duty. She provides you with tactical information, gives Master Chief pretty much his only emotional bond in the entire series, suffers through capture by the Gravemind, and in Halo 4 she even (SPOILER!!) gets breast implants for you to awkwardly ogle. She's pretty much the best online girlfriend since that one you had in high school who was totally real but she lived in Canada, that's why none of your friends ever met her.
Vivi is something special one of the few truly existentialist videogame characters, and one that actually is afraid of using his incredible powers. But besides having a deep, interesting personality and being one of the more colorfully-nuanced characters in Final Fantasy history, he's also an incredibly strong party member, being the only one capable of black magic 'n all. Plus, his "goodbye speech" at the end is one of the most heartbreaking moments in any game you'll ever play, and completes a brilliant character arc. Also, he's really just adorable-looking. Look at that hat! It's too big for his head!
Whether you pronounce it Tih-fa or Tee-fa (or something crazy like Ty-fa), Tifa remains one of the most badass and supportive sidekicks in any videogame (and she doesn't even need a giant, person-sized sword to hold her own). And even though her comically-proportioned body has made her a VERY dangerous person to do a Google Image Search for (TRUST ME), she's no stereotypical videogame bimbo she's a strong-willed, accomplished martial artist. Plus, it helps that she's the love interest that doesn't get impaled halfway through the game.
When he wasn't knocking back and forth in a barrel, gasping for air, Diddy Kong was one of the truly iconic sidekicks in any videogame. He had the unenviable task of hanging around with a giant, naked ape (except for the tie) and fighting an army of Kremlings, but at least he got his own racing game out of it (and had the worst luck ever he had a genie right there but got zero wishes). And the nice part about being "second banana" (ducks another barrage of tomatoes) is that no one will ever use his name when saying "It's on like Donkey Kong!" He's at least spared that indignity.
Even though Claptrap (the Fyrestone Claptrap, to be specific) acts essentially as a guide and sidekick to you in both Borderlands games, he has a pretty contentious relationship with you, and all humanity. In Borderlands' DLC, Claptrap raises an army bent on humanity's destruction and you have to fight him as a boss. In Borderlands 2, he's convinced you're merely a minion there to do his bidding, even when he's digging through trash by himself as you ignore him to gamble away your money at the cruel, unforgiving slot machines. Not that he isn't handy he does take down the Bunker's death wall. Anyone that takes down a death wall can't be all bad.