Friends
[The team] kind of told us that once you get past this point in the game, then at that point she starts to warm up a little bit toward Link. And then, from there, they gradually get closer and closer.
— Bill Trinen, speaking with 1UP.com
Link, the young farm hand turned-out-to-be legendary hero meets Midna in the dungeon of Hyrule Castle. When darkness fell across Hyrule, his protection from the goddesses — the Triforce of Courage — prevented him from melting away into the shadow; instead he turned into a wolf and passed out, to awaken in Hyrule Castle.
Although Midna seems unconvinced of his power — noting that he was not what she expected — she has no choice but to take him with her, as she needs his help to retrieve the Fused Shadows. The two partner up, as Link need's Midna's help and abilities to restore light to Hyrule and save his friends.
The real watershed moment for their relationship, although they grow closer and more amicable over the whole course of the game, is when Zant curses Link "permanently" as a wolf and, exposing her to the brilliance of a light spirit, almost kills Midna. Link rushes Midna to Hyrule Castle, where Zelda makes a sacrifice using the Triforce of Wisdom to save Midna. After this Midna has a great deal of respect both for Link, as a legendary hero, and for Zelda.
Zelda is the Princess matriarch of Hyrule. Midna appears to have met her for the first time offscreen and prior to meeting Link, presumeably as twilight fell across Hyrule and Midna was banished from the Twilight Realm. Zelda surrendered herself to Zant when he started his conquest of Hyrule in the hope of saving lives, and was confined to a tower in Hyrule Castle.
Initially Midna does not have a high regard for Zelda as a ruler. Aside from a comment that Zelda is not much better than Zant, she also refers somewhat scornfully to Zelda's "carefree youth" and "life of luxury" prior to Twilight Princess — maybe thinking of her own childhood in the Twilight Realm — but then says that she "shouldn't begrudge her the circumstances of her life" as she didn't choose them, much like Midna did not choose the circumstances of her own life.
Nonetheless, Midna seems to deem Zelda more integral to lifting the curse on Hyrule and saving both worlds than herself. She resists Zelda's sacrifice of power to save Midna when Midna is close to death, and this event breeds in her a deep respect both for Zelda and for Hyrule, which she vocalises towards the end of the game. It also has a big impact on her character development, and dispells her outward apathy as to the fate of Hyrule.
Foes
Lord, give me grace and dancing feet and the power to impress. Let me outshine the moon.
— "The Prayer" (Bloc Party)
Zant is the Midna to Ganondorf's Zelda in one way: in an inversion of Zelda tradition, the game focuses more time on him as a villain than on Ganondorf, even to the degree that he is set up to be the main villain of the piece (conversely, the player is left for much of the game to assume that Zelda is the Twilight Princess, when this is in fact Midna).
Zanr was a servant of the twili's Royal Family. With aspirations of being the next Twilight King and realigning the order of things as set out by the goddesses that were dashed when the Twili passed him over due to his greed, he was filled with a deep anger and despair. In this state — the state which had found the Twili banished to the Twilight Realm in the first place — he encounted Ganondorf, whom he elevated to the status of a god. He made a pact with Ganondorf, receiving great power in return for his servitude and cast the light world into twilight in line with Ganondorf's desire to fuse light and twilight into one world of darkness.
Despite the curse he has put on her and his obvious power (which she warns Link about), Midna states that she has "nothing but scorn" for Zant, and holds him in contempt. However, even with the Fused Shadows she is unable to defeat him at their first meeting. When he angers her — again note that this is the emotion which drove the creation of the magic in the Fused Shadows — by telling her that her curse can only be broken by defeating Ganondorf, and that Zant will be ressurected endlessly as long as Ganondorf lives, Midna unleashes this rage in "just a fraction" of the power in the Fused Shadows and destroys him.