the meaning of an existence
The Buster Sword represents both Zack and meaning of SOLDIER. It has an extensive history in the game. For Angeal it represented his dreams, his pride, and his honor which is why he only ever used it to fight important battles. When he died he passed it onto Zack, for Zack it became his connection to Angeal and the beliefs Angeal instilled in him (can you guess them?) his honor, dreams, and pride as a SOLDIER. Zack carried the sword and these principles all the way to his death, where he finally passed it onto Cloud, passing on with it both Zack and Angeal's dreams, honor, and pride. After Cloud defeats Sephiroth the sword holds a new meaning as a new beginning for Cloud. It is where Zack died a hero and passed on his legacy, enabling Cloud to become a hero as well. Which of course brings us full circle as the meaning of SOLDIER is to protect the planet as the people's heroes carrying with them the world's dreams, honor, and pride. The sword is also essentially a piece of Zack, which leads Cloud to speak to it during Advent Children.
It's hard to think of a time when Aerith didn't have her ribbon. Aerith's Ribbon wasn't always with her, and in fact was a gift from Zack during Crisis Core. Just as Cloud remembers Zack through the Buster Sword, Aerith carries Zack with her ribbon. Zack originally gave her the ribbon as a present on their first date after Aerith "saved" Zack's life. Once she ties it in her hair it stays and it can still be seen throughout the compilation and up until her death. The ribbon holds more significance to Aerith beyond that of a gift from a first date; this point is proven when Sephiroth stabs Aerith, which in turn causes her ribbon to become unraveled leaving a white materia to fall from it. The white materia is later identified as Holy, the only thing that would be able to stop meteor from destroying Gaea. The materia is without a doubt one of the most important relics on the planet, so why does Aerith carry it in her hair when hiding it in another part of her clothes would be just as easy? Clearly it is a sign of Zack's significant impact on Aerith.
Loveless is a play that tells the story of three friends who all give up something important to them in return for the "Gift of the Goddess". While the gift is a symbol that is apparently debated throughout the game, some possible meanings include Banora Apples which are supposedly amazing apples that better be made of gold or something based on the amount of times you have to hear about them while playing Crisis Core. They are apparently super rare and they only grow in, you guessed it Banora. They are considered by some to be the "Gift of the Goddess" mentioned in Loveless. Let's establish, these apples brought Genesis and Angeal together as friends despite their different upbringings. Another possible representation of the "gift" is Jenova Cells which can help stop the degradation [of Genesis]. Ultimately, it is believed that the "gift" is the "Pride of a SOLDIER" which Zack has had the entire game. Aside from deep meanings, Loveless also appears throughout the compilation on billboards and such.
The Cloudy Wolf is seen throughout Advent Children and often appears when Cloud is thinking about the past. This originally led many fans to believe that the wolf was a representation of Zack, just as the flowers and the water were symbolic of Aerith. It has since been "proven" through compelling evidence that the wolf doesn't actually represent Zack, but instead Cloud's guilt. Cloud feels guilty for failing the people he cares about (and cared about) most. Cloud remembers how he was too late to save both Zack and Aerith, which explains why he sees it when he thinks of them. He also sees the wolf when he finds Tifa unconscious after her fight with Loz. This can be explained by that fact that Cloud wasn't able to protect Tifa from him, and stop him from taking Marlene. Really though, while it would be nice to think it represented Zack, it just can't.