The ArbiterEditAlthough the two were never seen talking much together, Arbiter and Cortana were both considered "acquaintances" and were on good terms, but never really friends. Evident by Cortana refering to Arbiter simply as just an "alien" when she was with Todd. As of Season 6, Cortana seems to view Arbiter as a friend.
Developing a relationship with Todd, the two dated for some time behind Chief's back. After a while, Chief discovered that they were dating and set on a mission to find and kill Todd once and for all. Cortana respects her relationship with Todd, kicking Chief in the groin when she learned he was trying to kill Todd.
Travis and Cortana never even talked to each other at all throughout the series. Though she did call he and Chief "homophobes" after the two had called each other "gay" in Arby 'n' the Chief: The Movie.
Cortana seems to like Greg as a friend. She also doesn't seem to be repulsed by his appearance at all, unlike Master Chief and Arbiter.