It's our second Zelda game to make it onto this list. Link's Awakening actually has a bit in common with two other entries on this list, namely Majora's Mask and FFTactics Advance. Like FFTA, LA places you in a bit of a moral quandary about halfway through and like TA, the player is kind of left at the ending wondering if you did the right thing. The similarities with MM on the other hand are far more apparent.
The game actually has an interesting origin, as it was being secretly developed by some of the programmers who did LttP using ideas and concepts that didn't make it into the main game. They did this to blow off steam from the major projects they were working on. Soon what became a simple project started gaining more people helping out, and soon Nintendo game them permission to make the game. Wishing to make this more of a spin-off, the game incorporates villains and enemies from Mario and Kirby titles, and it was intentional to move the setting away from Hyrule and the main story. The Giant Egg idea was a scrapped idea for Ltt and found it's way into this game. The scenario writer Yoshiaki Koizumi, came up with the basic story and themes, and wanted to make the game feel like the TV series Twin Peaks, so he wrote the characters and the islanders to reflect this concept along with the underlying mystery surrounding the island.
Link's Awakening is a direct sequel to A Link to the Past. After saving Hyrule, Link goes on a journey and tries to cross the ocean before he is caught in a storm. When he wakes up, he finds himself on a strange island filled with colorful characters who worship the Wind Fish that sleeps in an egg on a mountain in the middle of the island. No one knows how long they've been there and have no real memory about the past. Only Marin, the young singer who found Link on the shore and helped him has ever really wondered what the world beyond the island is like. Link meets a strange talking owl (who would later inspire the different character in OoT) who convinces Link that his only way of leaving the island is to wake the Wind Fish by gathering eight spirit instruments and play a certain song to wake it up and get it's help off the island. About halfway through the game a certain revelation is made to Link by the monsters who guard the treasures that puts Link's journey into doubt.
So like MM, Link is ultimately transferred to a new place with a new villain, in fact Ganon, Zelda, and the Triforce are barely mentioned in passing and Link's real foe is original. The game is also less heroic fantasy and has more of a dark edge to it's story which is juxtaposed with a quirky cast of fun characters who are surprisingly cheerful considering what the story is really about. There is also a greater emphasis of talking and dealing with the locals, as often the temples are connected to them in some way. Marin herself is more prominent figure in the plot than previous NPCs in the franchise.
The game also serves a s a bit of a bridge between A Link to the Past and Ocarina of Time, as the game is loosely based on the tech of LttP, but it also brings in many elements that would become major features in OoT. For instance, the Ocarina and the need to learn various songs to progress the quest, actually debuts in this game. The game also introduces the Mario Bros. expy's and along with Marin herself, will come to be expy's again in OoT as Maron and the Lon Lon Ranch crew.
The core gameplay isn't terribly different from mainline Zelda titles, but there are more experimental elements in the game than typical Zelda titles. The game plays around with Mario style side scrolling elements and there are actual a few Mario enemies like Goombas and Chomp Chomps that makes appearances in this game. Even King Wart from SMB2 (also on this list) appears as the King of the Frogs and teaches the Frog Song to Link. There is also a cameo from a character from another Game Boy title that never made it out of Japan.
Probably the coolest feature the game brought, which for reasons I'll never fathom, didn't become a major feature for the franchise and only ever showed up in one other game, is the ability to use two sub-weapons/item by replacing the sword with one of them. This ends up creating some interesting combinations like combining the Bombs and Bow to make Bomb Arrows, or using the Pegasus Boots running mechanic in conjunction with the Roc Feather's (debut) jumping mechanic to greatly expand Link's mobility and create more clever means of getting around the island.
While Link's Awakening is kind of doomed to be always overlooked by Zelda fans since it's not a console entry and more of a spin-off, the game is really well designed and has a great cast and story with it. It was a sheer blast playing through this entry a few years ago, and I'm still kicking myself for taking so long to get around to it.