Watch Da Birdie
I buy cakes for myself on my birthday it's not weird lots of people do it I bet
If you ask someone what they'd consider to be the "Zelda Canon" (in terms of what games are important to the movement of the series, not talking about timeline shenanigans), most would likely say Legend of Zelda, Link to the Past, and then Ocarina of Time. These three games are usually held up as the greatest Zelda has to offer, setting the standard for various games to follow and generally agreed upon to be all great games in their own right. Now, that's not to say that the others aren't important or enjoyable, they definitely are, but these are usually the three held up as the being the biggest influences in determining the evolution of the series. Legend of Zelda set the ball rolling, Link To The Past refined and set the formula in-stone going forward, and Ocarina of Time transported the series to 3D.
The other games in the series, in comparison, are more self-contained, and while they do add new gameplay and thematic elements to the series, usually they're not as influential. Wind Waker did inspire quite a lot of future games in terms of the art-style, such as Minish Cap and Phantom Hourglass, but overall many of the gameplay elements Wind Waker introduced didn't exactly become commonplace, and I feel the art-style didn't inspire future games, rather the future games just re-used it, which became a bit annoying eventually. Minish Cap used it to great effect since it was sprite-based, and thus not just copying Wind Waker, but Phantom Hourglass and Spirit Tracks was a bit displeasing since it showed that a weaker system really didn't go well with Wind Waker's cel-shading. Skyward Sword is the most recent "main game", though, and did feel like a notable departure from the series in many ways, so I wouldn't be surprised if for better or worse it could set a new standard for the series style and might be more influential than it is at the moment. I know this sounds bad at first, but there were enough good ideas in Skyward Sword I wouldn't mind becoming more influential such as the denser overworlds, upgrade system, and stamina system.
However, I argue that there is one game that deserves to stand among the main three as being equally influential when it comes to the direction the series has evolved in, and doesn't get enough credit---Link's Awakening. You see, gamers in general have a weird notion towards handheld entries (excluding series that are handheld focused like Pokemon), where handheld entries are deemed as simple detours from the main meat of the series, and thus aren't as important. This is a double-edged sword...I feel this allows handheld entries to take bigger risks with the formula than the console entries can get away with, as people seem to be less critical of them when they break the mold because their development is viewed as being sort of a bridge between the bigger games. When you have big Triple AAA console Zelda games, and one is disappointing, it sticks out. But with the handheld entries, a bad entry is easier to view as a bump in the road, and not indicative of a decline in overall quality for the series. A lot of people don't like Phantom Hourglass, I'm not one of them, and a lot of people don't like Skyward Sword, but I think if you polled people, I think the hostility and "ruined forever!" cries would be aimed at Skyward Sword far more than Phantom Hourglass.
Anyway, because Link's Awakening is a handheld game, I don't feel it gets the credit it deserves. It's easy to just see it as a quirky gaiden game, people definitely love the game, but usually when you ask people why, you just get "it's fun!", or "it's just so different!", like what you hear with Majora's Mask. But while Majora's Mask is a departure from the series, and much of what it introduced really didn't catch on (although that may chance with Zelda Wii U perhaps...), I think Link's Awakening actually ended up being far more vital to the series, and more influential than people really notice. In fact, Anouma has gone on record saying that without Link's Awakening, Ocarina would be a "very different game". So, let's look into this a bit further.
Before I start, a bit of background info when it comes to my relationship with the Zelda series. I'm a bit hazy on how everything went down, but I do know that I never actually played the NES Zelda games till they were re-released on that Gamecube Anniversary Disc, and even to this day, regrettably I've never actually played them beyond a few minutes at the beginning. My first Zelda experience was playing Link to the Past, although it was "just a game" to me when I first played it as I wasn't cognizant that it was part of a much larger franchise, and I didn't understand its impact. The first time "Zelda!" really hit me was when I got Ocarina of Time, and then going back and playing Link to the Past changed how I viewed it...I could see its "evolution", and how this series came together. Not too long after, I believe it was in February (this is where my memory fails me a bit), I got a GBC for my birthday, and got Link's Awakening DX. At this point, I had a new fondness for the Zelda series, and had a lot of fun playing Awakening, but because I played things out of order, how unique Awakening was didn't really hit me. The only thing that really stuck out was that Link could actually jump, rather than it being 'on-rails' like in Ocarina. I've been a Zelda fan since then, and have played all of them to near completion more or less (admittedly I'm bad at finishing games...I've never fully beat both Oracles together, Phantom Hourglass, Spirit Tracks, Skyward Sword, or Link Between Worlds), but Awakening ended up being my most cherished.
In retrospect, Link's Awakening actually is a pretty standard Zelda, mechanically. It began as a port of Link To the Past (would've loved to see them pull that off though), which is probably why it follows the standard eight-dungeon formula, and most of the items are recycled from LTTP. The only real new item that's of any use in gameplay is the Roc's Feather, which I think does shake up things quite a bit. Jumping is such a standard game mechanic, but when a series normally avoids it, when a game actually throws in manual jumping for the player, it's actually sort of fun and exciting to see. I was glad to see Roc's Feather, and the Roc's Cape, return in Oracle and Minish Cap with new functionality, and disappointed to see it was dropped in Phantom Hourglass. Although I can understand this...I don't think it'd work quite as well with the touch control PH and ST went with, but I was sad to see Link Between Worlds dropped it as well. The Tornado Rod added some neat vertical movement, but it doesn't compare with free jumping in my opinion. I've said this before, but I'd love a Zelda where jumping plays a major role.
The only other direct gameplay mechanic Link's Awakening adds are the "power-up items", perhaps borrowing a bit from Mario, Link can collect two items---the Guardian Acorn and the Piece of Power---which temporarily grants him increased defense/attack for a limited time, complete with a power-up jingle like the Star Man. This is kind of an odd mechanic, though, which doesn't quite fit with Zelda, and so it's never really returned in later games. You have a few potions that do similar things, such as in Skyward Sword, but just finding power-ups as drops from enemies has been absent except for Four Swords Adventure, where it goes quite well with the more arcade-style, and Hyrule Warriors, where it also fits the action style better.
Ultimately, Link's Awakening doesn't have that "gimmick" that most of the other Zelda games tend to have. Usually when you ask someone to describe a Zelda game, they'll usually tell you about the big mechanical element unique to it....Ocarina of Time's time child/adult dichotomy, Wind Waker's wind manipulation and sailing, and Twilight Princess' wolf form. But Link's Awakening's gimmick isn't its gameplay, it's its unique setting and themes, which stuck out at the time...but nowadays, they actually perhaps feel a bit more in-line with the following games.
Link's Awakening is the first, and only Zelda apart from Majora's Mask, to not (except for a few cameos) involve Zelda, Ganondorf, or the Triforce. While other games haven't gone to the same extent Link's Awakening did, it did sort of inspire future games to break away from the rigid trio. Zelda ends up being kept still more often than not (it's her series, basically), but it's not too uncommon for the Triforce to not factor into the plot beyond being just implied, and Ganondorf has sat things out in quite a few games since. It also takes place outside of Hyrule, which is also a more common element, and I'd argue has actually sort of become the norm if you think about it. Majora's Mask takes place in Termina, the Oracle games take place in Holodrum and Labrynna, Wind Waker and Phantom Hourglass takes place on the Great Sea, Spirit Tracks takes place in New Hyrule, and Skyward Sword features the land before it became Hyrule as well. Some of those are cheating---but really, just regular old Hyrule has only prominently been featured in Ocarina, Minish Cap, Twilight Princess, and 1/2 of Link Between Worlds.
Another thematic element of Link's Awakening is its quirky and colorful cast of NPCs. Prior to this, Zelda had sort of a bland collection of NPCs. Most of them were simply there to just give you a straight-up hint, or weren't that stand-out except for the few blessed enough to get a memorably butchered translation. Link To the Past had a couple memorable ones, like the flute boy, but overall no one really played it for the characters. Link's Awakening was the first to have a real lively and odd world, "inspired by Twin Peaks", and I feel following this that became the norm. Sure, Ocarina of Time and Twilight Princess have a "realistic" style, but even then if you think about it, most of the NPCs are over-the-top and cartoonish. I think this is something I really enjoy about Zelda---for all its flaws, Skyward Sword had some great personalities (not Fi) hanging around the few town areas, that made me enjoy my time with the game despite it being a bit shallow beyond that.
Three of the characters introduced in particular sort of became synonymous with Zelda: first off, Marin and Tarin. Marin, who served as a Zelda stand-in (and the first time we really saw Link have a relationship with another character since his interactions with Zelda in past games were limited), is an iconic character, and inspired Malon in Ocarina of Time, who she herself inspired other similar characters throughout the games. Tarin, the Mario look-alike, is less important, but also influenced the character of Talon, who usually isn't far behind when Talon appears. Then, of course, you have the Owl. In Link's Awakening, a mysterious overseer who helps Link in his quest, and was brought back in Ocarina of Time as Kaepora Gaebora, and like Talon and Malon a variation of that character appeared in a few other games too.
The Owl has since disappeared from Zelda since Majora's Mask, and I actually think this is because he's a bit redundant---you don't really need him telling you where to go when you have Partners like Midna and Fi who can do that as well. Even in Ocarina of Time, he seemed a bit at odds with Navi who served basically the same function. The reason I bring this up is that I feel Link's Awakening also began the tradition of a "Partner", but in a more subtle way. Throughout Link's Awakening, there are quite a few characters who end up following you---Marin, the ghost, and the Flying Rooster. These characters temporarily give Link a friend to travel with, and also help him in various ways, which became more commonplace with the Partners. It's another addition I like, most of the time, as Link not being on his own makes the game more interesting. Sure, they mess it up sometimes like with Fi, but overall I'm excited to see who will be helping Link out in each game. They hit more than they miss, for me.
Music also plays a more vital role in Link's Awakening, which became another key element of Zelda. Sure, there were musical instruments in previous Zelda games, but they were usually a minor item with a simple function, such as just using it to warp in LTTP. Here, your ocarina now has the ability to play three different songs, and magical musical instruments are a key component of the plot, which is now a Zelda tradition. The Ocarina of Time, the Wind Waker, and the Goddess Harp, all seem like an extension of this. And who can forget the first time you hear the full version of the Ballad of the Windfish? Gaming's most magical moment, easily.
Link's Awakening was also the first Zelda to get a bit silly with how it set the world up, whereas the previous Zelda games were much more straightforward and typical fantasy. The weirdest thing in LTTP was probably the fact Sarashala used speakers to talk to you, but overall the world seemed pretty typical lite-Medieval. Link's Awakening sort of spun this around, throwing in a lot of anachronistic elements like a crane-game, camera, and telephone, and future Zelda games have also sort of branched away from adhering to a grounded fantasy setting. Ocarina didn't go too out of its way, but look at Majora's Mask and Skyward Sword, and how they have quite a few odd modern elements thrown in. There's also the Mario-crossover elements in Link's Awakening (although Manhandla is according to the Japanese manual of the Legend of Zelda a species of Piranha Plant), which also popped up in Ocarina of Time, and sort of see a return in Link Between Worlds, with Ravio's similarity to Nabbit perhaps being a cute nod to this.
Finally, there are three major gameplay elements, but not directly related to the main game, that Link's Awakening created. First, the infamous "Trading Quest" that has basically been in every Zelda since, and is usually a pretty fun element to take part in. Finding the people who want the items, figuring out what to trade, it's a nice game-length puzzle to fill out the time. Second, the "Item Side Quest", where there's an extra little item to look out for as you journey through the world. In Link's Awakening, it was the seashells, and it expanded from there to include things such as bugs, fairies, and recently Maimai. And finally, the fun little fishing game, which was expanded in Ocarina of Time and had a nice return in Majora's Mask 3D.
There's a lot of little elements in Link's Awakening I also think perhaps inspired later games---such as the Wind Fish Egg being thematically similar to the Moon, an omnipresent doomsday device (although less intimidating---but overall I think these are the main points which show that Link's Awakening shouldn't be seen as a quirky gaiden game, but rather a cornerstone of the series. While I think Link's Awakening is pretty much perfect, I'd be lying if I didn't say I hope they take the Link Between World engine and make a great homage to Link's Awakening next, at least in terms of capturing its tone and style. But then I think, and perhaps every Zelda has a bit of Link's Awakening in it.