Arguably the most popular AI ever created, Cortana is Master Chief's Yoshi. Ok, wait. Let's put the heretic chants away for a second and just consider the possibility. How far do you think Master Chief could have gotten in the Halo series without Cortana's help? Sure, the Chief didn't always have Cortana in his head and he's more than capable as a soldier who's always had a knack for getting the job done against all odds. But when we consider the events of the Halo games beginning with Halo 1, do you really think our hero would have made it off that ring without his guardian AI guiding him along?
Yoshi or not, Cortana looks after Master Chief in the most genuine of ways, even though she's not able to help him in any physical way (at least, not until the end of Halo 4). The biggest strength Cortana utilizes is the power of speech. More than anything else she does through the game, she talks to Master Chief. In fact, it's her voice that many gamers have found so appealing for various reasons. Microsoft most have picked up on that since they chose her to be the Siri of their Windows Phone. There are many periods of isolation throughout the games where Master Chief is completely alone, save for Cortana. As in real life, sometimes it's comforting enough just to hear a friendly voice. The Chief and Cortana have an interesting relationship that difficult relationship to categorize at times, but that's not a bad thing. In Halo 1, Chief and Cortana acted more like siblings who doubled as partners in crime, getting into all kinds of trouble and finding ways to get themselves out of it again. By the time Halo 4 rolled around, the relationship had begun to develop some romantic undertones.
Thanks to technology, Cortana has never been more expressive than she was in Halo 4, so you could pick up on her emotions easier than ever. Just look how far her design evolved from the first game. She even changed hues! It could be that as her color gradually changed, so to did her emotions? Maybe it was just the rampancy. Romance or not, Cortana always has the Chief's back as gaming's first Ride or Die AI. Fancy that.