This is a list of theories that has to do with both The Legend of Zelda: The Wind Waker and The Legend of Zelda: Phantom Hourglass together.
Cyclos/Golden Chief Cylos TheoryEdit
It is likely that Cyclos is somehow connected to Golden Chief Cylos from The Legend of Zelda: Phantom Hourglass. This is likely because they are both similarly named overgrown frogs, who have wind-related powers.
Princess ZeldaEditThe relationship Zelda has with Link is close, possibly her closest. A popular theory among fans is that of a romantic relationship between some of the Zelda and Link characters in the Zelda series. Although never explicitly confirmed in a video game title, this theory is based on hints given in the games, interviews with the game creators, and content of the animated series, comics, and manga (although the last three are generally considered non-canonical).
One hint of a romance between Zelda and Link is given at the end of The Adventure of Link, when the awakened Princess apparently kisses Link under the falling curtain.
Some cutscenes in Ocarina of Time featuring the two together have been interpreted as signs of an attraction. While Link and Zelda are escaping Ganon's Castle, Zelda will additionally show her concern for Link by shouting out whenever he is hurt. Moreover, in the game's final scene, Zelda and Link are floating in the sky together, sharing a decidedly sentimental (if not necessarily romantic) moment where Zelda apologies for involving Link in the events of the game and seems saddened by the situation. She also stated that she will not forget the time she spent with him in the Child Timeline as shown in Majora's Mask through Link's memory.
In addition, if the Oracle games are played as sequels to each other, the ultimate ending sequence shows Zelda lightly kissing Link on the cheek. Link swoons while hearts float above the pair's heads, and Zelda looks away, blushing. In The Wind Waker, when Zelda is asked to stay in hiding in Hyrule Castle while Link restores power to the Master Sword, she waves goodbye to Link, asking him to be careful.Spirit Tracks features several moments that can be interpreted romantically. Early in the game during the Graduation Ceremony, Zelda walks into the room in front of Link, who is bowing down respectfully. Link then looks up and gasps, blushing at her in amazement. He is then scolded by Chancellor Cole for raising his head without permission. Later, when Zelda's spirit is separated from her body following the first encounter with Chancellor Cole and Byrne, Link is the only one who can see her besides the Lokomos, demonstrating a clear and strong bond between himself and the Princess. After Zelda and Link defeat Byrne in the Tower of Spirits, Byrne, disbelieving, comments that he was beaten by two humans. Zelda, while still possessing a Phantom, says that when she and Link combine their strength, no one can defeat them. Link turns to her, surprised. The background turns white and Zelda's Lullaby plays as they both laugh and high-five, gazing at each other all the while. Toward the end of the game, before the final battle against Malladus, Zelda is reunited with her body, and is no longer able to levitate. Link runs underneath her to catch her as she falls, and she lands on top of him and knocks them both to the ground as well as knock Link out for a few seconds. Upon awakening, Zelda, overjoyed to have her body back, embraces Link, causing him to blush. Finally, after Malladus is defeated, Zelda and Link watch Anjean and Byrne's spirits ascend to the heavens. The camera then lowers to show Zelda and Link holding hands while Zelda's Lullaby plays in the background. After the credits, a short cut scene shows Zelda gazing at a picture of Link on the Spirit Train with her flying beside him, which she keeps on her desk. she may also wave at Link depending on his answer to a question Zelda asked before.
Skyward Sword has several noticeable romantic moments between Link and Zelda. Early in the game, Zelda wants Link to be the first to see her outfit for the Wing Ceremony. She worries over him and she does not want him to fail at becoming a knight. When Link's Crimson Loftwing is hidden by Groose, Zelda assists Link in finding his Loftwing. After Link wins the Wing Ceremony, Zelda jumps off the ledge and Link catches her almost as if she was expecting him to. She then congratulates him on winning. Afterwards, Zelda mentions that she is very happy to be atop the Statue of the Goddess with him. She also gets extremely close to him and almost implies that the two are to kiss, before she pushes him off the statue. Afterward, Zelda bashfully asks Link to go out flying which they do. She then tells Link how amazing the day was, and that she would remember it forever. At the Temple of Hylia, when Zelda states she must seal herself to keep Demise in place, she sheds tears of sadness and states before all this, she was happy just being with Link on Skyloft, demonstrating a deep level of feelings for Link. Link desperately tries to stop her and when she is sealed, Link lowers his head in sadness, showing his deep feelings for her. Much later in the game, when Link releases Zelda from her sealed state, Link runs up and catches her from falling and both of them hug and walk out smiling at each other, holding hands, before Ghirahim ruins the tender moment. During the ending, Zelda asks what Link will do now. Link sweetly smiles at her while their Loftwings fly off toward the sky, implying that he chose to stay on the Surface to live with Zelda.
A Link Between Worlds features some gossip told to Link by the Rumor Guy. He tells Link that one of the castle staff had seen Zelda sneaking off every night. When she followed her, she saw Zelda staring at the painting in Hyrule Castle depicting the Link and Zelda from A Link to the Past cuddling with each other, implying they became more intimate with each other. This also hints the Zelda in A Link Between Worlds wants to have a similar relationship with the Link of her time.
The game creators also seem to be fond of the idea of romance between the characters.
Though never directly stated in-game, Shigeru Miyamoto revealed in an interview conducted by Famimaga 64 that Navi is jealous of Princess Zelda and has feelings for Link.
Another less popular theory among fans is that Link and Zelda are related by blood, either as siblings or more distantly. Even though rumors to this effect started with the infamous "Save the Princess... Zelda is your... ... ..." line from A Link to the Past (later reported as a mistranslation), the theory generally revolves around the Link and Zelda from Ocarina of Time.
A possible indication of a blood relation between the two in Ocarina of Time is their physical resemblance: they both have blonde hair, blue eyes, and similar facial features. They also have similarly shaped heads. Graphics limitations could be responsible for some of this similarity, however. Certain dialogue could also be perceived as implying a blood relation: the ghost Sharp comments that Link reminds him of Zelda, and that Link "may have some connection with the Royal Family". Link's connection to the Royal Family is highlighted throughout the game, with Link often playing Zelda's Lullaby to verify it. The fact that Impa agrees to teach a strange boy a song only Royal Family members are allowed to know could also be interpreted as a hint at Link's blood relation to Hyrule's Royal Family. 
Additionally, Zelda seems to recognize Link's name upon their first meeting. This could be attributed to her prophetic abilities, although the boy in her dreams seemed to be a largely abstract figure, with no defining traits aside from the presence of a guardian Fairy and a Spiritual Stone. This line of dialogue has often been regarded as a sign that the two have met before, although this could only have occurred when Link was a baby per the Deku Tree Sprout's account of Link's coming to Kokiri Forest. It is also worth noting that while the King of Hyrule is clearly identified as Zelda's father, no mention is made of a Queen. Meanwhile, Link's mother is stated to have died shortly after reaching the forest, but no information is given concerning his father. Given these facts, it is possible that Zelda and Link share the same parents, making them siblings.
It is speculated by some that alternate worlds such as the Twilight Realm and Termina may be unaffected by the timeline split. However, while these two realms are alternate dimensions, there is no evidence to support the idea that they exist outside of linear time. Both realms have demonstrated the ability to receive beings from the Child Timeline and return them to the Child Timeline when they exit back into Hyrule. There is no reason to believe that these two realms would only exist as a single timeline, or that they could "prioritize" inputs from one timeline, and later output these into both the timelines.
In addition, the renowned Youtube show, Game Theory, dismissed the Zelda Timeline, particularly the Defeat Timeline (in where Link fails on his quest) on the grounds that "the hero cannot be simultaneously victorious and defeated". Elaborating, he explained that with Link defeating Gannondorf, two perfectly possible timelines are created; However if Link dies at any point in his journey another separate timeline is created. Explaining that the only way for all 3 timelines to exist is the Many Worlds Theory (the theory that all possible pasts and futures exist in separate timelines).