The first The Legend of Zelda game created the series and was one of the first true Action Adventure and open world games, establishing the formula of underground dungeons on a connected overworld. A Link to the Past then defined Zelda as we know it by adding the classic charm of the series and many elements that are seen as typical for a Zelda game, like cutting grass, opening treasure chests or lighting torches...
Ocarina of Time then took what A Link to the Past had created and successfully transferred it into the third dimension, revolutionizing 3D gaming on its way with context sensitivity, the Z-targeting and more. It also introduced many recurring things to the series like Epona or the different tribes, shaping the series on top of what A Link to the Past already had created.
Breath of the Wild now fully returned to the open world origins and showed how it's done by using the player's urge to explore, where you can freely climb almost everywhere, look for a destination and then glide there. It also introduced a physics engine to the series, which is used for many of the game's puzzles, as well as a heavy focus on mini dungeons and resource management. And all of that got wrapped by a focus on ancient technology, which essentially became the new magic.
Now, there have been many Zelda games between Ocarina of Time and Breath of the Wild, thirteen to be exact, where the series certainly didn't stop to evolve. There have been many experiments with gameplay, controls and art style, creating what's one of the most diverse series in gaming history. But there also has been a big focus on one-game-gimmicks, which helped to make a game unique within the series, but which rarely ever had a lasting impact.
However, there's still one Zelda game in all of this, where you could make an argument that it had this lasting impact: The Wind Waker.
Back when Breath of the Wild was still in early stages, producer Eiji Aonuma mentioned, how the development of The Wind Waker HD influenced the new Zelda game (see here or here). And this shows. Breath of the Wild took many of the things that first were introduced in The Wind Waker and made them bigger and better.
Cel Shading
Probably the most controversial part about the original game were the visuals. The Wind Waker took the Zelda series in a whole other direction with its toon style, which wasn't to every fan's liking. When Twilight Princess later was revealed at E3 2004 with its more "realistic" and grittier art style, the audience cheered in joy and everything seemed right again. But over a decade later things look quite differently. The Wind Waker's art style riped like a good wine, where the game still looks beautiful today, while the visuals of Twilight Princess haven't aged that well.
The toon style also fully stuck with the series, where the Four Swords games, the Nintendo DS installments and Tri Force Heroes adopted it for their character and enemy designs. Toon Link even exists next to Link in games like Super Smash Bros. or Hyrule Warriors and fully has his own individual charm as a character.
While Breath of the Wild didn't use the toon style, it did find a common ground by using a realistic art style with cel shaded graphics. It has the mature appeal of games like Twilight Princess, but at the same time it also comes with the timelessness that the visuals of The Wind Waker prove to have. It's the best of both worlds.
A Seamless Overworld
One of the most impressive feats about Breath of the Wild is how the game handles its massive world, where other than the outer borders there are no limits. You can walk seamlessly between the areas without any loading times at all.
Due to technical limitations Zelda games usually segmented their worlds into smaller areas, rooms and screens even, but The Wind Waker was really the first Zelda game to attempt a seamless overworld similar to the one in Breath of the Wild. Of course the technical limitations were still in place at the time, where the game tried to hide them by letting you travel over an ocean and islands were loaded, as soon as you get closer. But the approach was there. You can travel from one corner of the map to the other without ever changing "screens".
While Twilight Princess had one seamless passage through Hyrule Field, where you can travel through the world in a circle without visible loading times, most of the overworld was still segmented into "rooms", especially around the villages. And while Skyward Sword featured a set of larger areas, they were all fully segmented from each other.
Breath of the Wild now finally returned to the seamless approach and has a world similar to that of The Wind Waker, but with a massive mass of land instead of a mass of water. It even took the seamlessness to the next level with villages, where the insides of houses were for the first time in the series accessible without any transitions. However, the big downside were longer loading times when teleporting or entering a Shrine of Divine Beast, where the game even saw a dedicated loading screen for the first time in the series.
The Deku Leaf
Even though it's one of the most versatile items in the series, the Deku Leaf often gets overlooked. It has two main functions in The Wind Waker, which got split later in the series. It can shoot gusts, which was copied by items like the Whirlwind, Gust Jar and even the Korok Leaf in Breath of the Wild. With this ability it gave a glimpse at what physics could achieve in Zelda, where you could influence many things in the environment with this item.
But it's really its second ability that was ground-breaking for the series: the gliding. It introduced a new level of freedom in movement, where you could use any vantage point to glide on top of rocks or buildings. At the time it was limited by the magic meter and the nature of the ocean world in The Wind Waker, but Breath of the Wild took this idea and brought it to the next level with the Paraglider item. Combined with the free climbing ability, it's a big part what makes Breath of the Wild so fantastic.
Scope and Camera
The Sheikah Slate in Breath of the Wild has many useful features, along them are a scope to view the distance and a camera to take pictures at any time. Technically, both of this got featured for the first time in the series in Majora's Mask, where you had the Picto Box as an item and where you could use a telescope in certain locations. But The Wind Waker fully expanded upon that.
The Telescope became an item in your inventory to be used at any time and the Picto Box was featured in one of the most extensive side quests in the series: the figurine collection of the Nintendo Gallery. This can be compared to collecting pictures of everything for Hyrule Compendium in Breath of the Wild, though that's probably closer to the scanning in the Metroid Prime Trilogy.
Anyway, The Wind Waker HD even added funny selfies to the camera feature, which made a return in Breath of the Wild as well.
Boating
While past Zelda games let you travel via raft in certain places, The Wind Waker with its ocean world turned a boat into the main method of transportation for the first time in the series. The sequel, Phantom Hourglass, brought the ocean world back and let you travel via steam boat, which then got transformed into a train in Spirit Tracks. So, this certainly left a mark on the series.
Unlike in Breath of the Wild, this was really the only means of going from one island to the next, while Breath of the Wild doesn't even have a dedicated boat for its ocean areas. Instead it brought the traditional raft back, where it's subject to the game's physics and can be propelled with the Korok Leaf item. A real boat probably would have been more convenient, however, and it's thinkable that a sequel to Breath of the Wild might introduce a mechanical boat spawned by a Sheikah Slate Rune similar to the Master Cycle Zero.
Lookout Platforms
Having a massive open world like in The Wind Waker or Breath of the Wild comes with a price. Filling the environments with content isn't an easy task and often leads to repetition, where certain elements get copied and slightly altered. In Breath of the Wild these are for the most part the many Sheikah Shrines and Towers, but also the different enemy camps, which are made of skull-shaped caves, campfires and even larger constructs of watch towers, both on land and in the ocean.
These towers aren't exactly new, but were a recurring structure in The Wind Waker as well, where many of them can be found all over the Great Sea. Often they are inhabited by Bokoblins, but they might also feature cannons, Wizzrobes or gliding puzzles.
The lookout platforms aren't exactly popular and are more a sign of cheap open world design, but they were prominent enough to be featured in Super Smash Bros. for Wii U:
And that's something, right?
Expressive Enemies
Lookout towers and rafts essentially served as little homes for Bokoblins, who were scouting the oceans as pirates and got introduced in The Wind Waker as a new, expressive type of enemy. Alike, Moblins were patrolling the Forsaken Fortress and you could really see the surprise on their faces, when they eventually spotted you. Enemies never felt as alive before The Wind Waker, where they became a real part of the world, instead of simply being nuisances on your way through Hyrule and its dungeons. It was fun to interact with them in different ways, like making their butts hurt.
Twilight Princess didn't really capture this, where even its Bokoblins felt quite dull overall. In Skyward Sword the Bokoblins felt more alive again, but the game still didn't reach the same level of aware enemies that The Wind Waker offered.
Breath of the Wild now brought the Bokoblins back to old glory, leading their little lives around campfires. The same can't really be said about the Moblins, who still were a lot more charming in The Wind Waker, but at least the Lizalfos became more sentient and interactive alongside the Bokoblins. Lynels leave a big impression as well and the Guardians, while being machines, still felt very alive and like an important part of the world that keeps reacting to you in its own way.
Spoils and Treasures
Defeated enemies in the Zelda series usually drop Rupees, Hearts and ammunition (like Arrows or Bombs). It wasn't until The Wind Waker that enemies also might drop special dedicated items, like ChuChu Jelly. It introduced a Spoils Bag for this, which could store up to 99 of different enemy spoils. Those spoils had different purposes, but also acted as an alternate currency, where some of it could be traded for Rupees.
Sadly, this idea was completely dropped by Twilight Princess, but the Nintendo DS Zelda games later introduced treasure items with a dedicated menu screen, partly based on the spoils from The Wind Waker. These treasures weren't dropped by enemies, however, but were instead found in treasure chests, found in the environment, purchased in shops or won in minigames. Skyward Sword then created a mix of both, where some treasures were dropped by enemies with a certain chance and others were found in the environment or a prize for minigames. It also added a collection of insects on top of that.
Breath of the Wild now took all that and blew it out of proportion with over a hundred of different "materials" to collect for cooking, trading or enhancing your armor. Some of these items could even be dropped again for different uses, e.g. creating campfires. It's a big feature of the game, but it all started with the Spoils Bag in The Wind Waker.
Enemy Weapons
Spoils weren't the only thing that the enemies in The Wind Waker left behind. For the first time in the series you could actually disarm the enemies and use their sticks, swords, machetes, spears or clubs. You weren't able to put these weapons in your inventory, but they certainly provided a nice diversion from the usual sword play.
Sadly, this didn't see a return for a long time in the series. Twilight Princess and Spirit Tracks featured special mini bosses, where you would obtain their weapons after the fight, while Skyward Sword only lets you use an enemy's weapons during a single boss fight. And it was a shame that the games didn't do more here.
Breath of the Wild finally returned to form, where you can obtain and use the weapons, shields and bows of almost every enemy in the game (the exception being the big bosses). You can even store them in your inventory this time and use them anywhere to your pleasing. On top of that Bokoblins, Moblins and Lizalfos are able to use any weapons they might find against you.
As a downside the weapons might lose some of their ridiculousness, like Toon Link swinging a sword that's twice his size, because the weapons scale based on the size of their wielder. So, that massive sword used by a Moblin will be normally sized in your hands... But it was certainly a giant step back in the right direction.
The Rito and the Koroks
Ocarina of Time characterized and shaped the different tribes of Hyrule next to the Hylians. The Sheikah, the Kokiri, the Gorons, the Zora (as a peaceful tribe), the Gerudo and even the Deku got introduced and established in this game. This remained for the most part and especially the Gorons were so popular, they got featured in almost every Zelda game after Ocarina of Time.
When later Zelda games introduced new tribes or races, they usually didn't become a staple in the series. The most prominent ones were developed around a one-game-story like the Minish, the Twili or the Lokomo, where it's unlikely that they will ever be featured again. Others were merely there in one or two games, like the Tokay, the Subrosians, the Anouki or the Zuna. Ask any Zelda fan about the latter and you most likely will look into confused faces...
Skyward Sword had probably the biggest failed attempt at introducing new races with the Kikwi, the Mogma, the Parella and the Lanayru Mining Robots. But being featured in an origin story, where the rest of the series never starred them again, put them in a bad place to begin with.
The only real potential apparently came with the Koroks and Rito featured in The Wind Waker. However, they evolved from two races from Ocarina of Time, the Kokiri and the Zora, which connected them to the past in an interesting way. It also helped that a representative of both races followed you through a part of your adventures and could even be controlled by the player.
The Koroks and the Rito were something to remember and both returned now in Breath of the Wild alongside the Gorons, the Zora, the Gerudo and the Sheikah. Zoras and Ritos now exist alongside each other, but they were different enough to begin with. And Koroks now exists in the hundreds, creating the most extensive collectible quest in the series yet with lots and lots of charming little puzzles. And after Breath of the Wild it feels like we haven't seen the last of these races.
Beedle
Last but not least, The Wind Waker introduced a recurring character to the series, who really has his own charm and isn't despised by many of the fans (yet): Beedle. The funny merchant traveled the Great Sea in his endless quest to make money, but also had appearances in The Minish Cap, Phantom Hourglass, Spirit Tracks, Skyward Sword and finally Breath of the Wild. To be fair, his last appearance wasn't his best one, where his constant nagging for rare beetles in your inventory was rather annoying, but he's still the same unique character with the funny voice acting that we know and love.
Thaaaaaank youuuuu....!!!
Conclusion
The Wind Waker isn't among the best-selling Zelda titles and with its art style and setting it split the fanbase, when it originally was released. Still, it had a lot of influence on the new and successful Breath of the Wild and the series a whole, where it could be viewed as one of the few pillar games that really shaped Zelda into what it is today.