One of the weirder entries in the series, and one of the best: Link's Awakening stranded Link on an island to wake up a psychic whale/fish that was creating the entire island in its dream (which, on an unrelated note, would have been a better ending to Lost). What's truly incredible about the game is that it is a full-fledged, huge Zelda game that somehow fit into the Game Boy's extremely-limited software capabilities.
Also, this is the game that introduced fishing into the Zelda series, leading to the deaths of untold hundreds of innocents as Link fished away the days while Ganon and his minions led Hyrule through multiple reigns of darkness.
The most recent Zelda game met with a lot of criticism over Fi (who somehow surpassed Navi in the eyes of many as the most annoying companion) and the motion controls (that achieved 1:1 with the Wiimote), amongst others as well as a lot of acclaim. It's not too surprising, considering this game came out in celebration of the Zelda series' 25th anniversary after 25 years of some of the most consistently incredible and genre-defining adventure games, things start to feel a little dull, so you have to complain a little (although, really, the tutorial portion of the game makes you long for the days when a crazy old man would just hand some kid he never met a sword and shoos you out into a nightmare labyrinth crawling with monsters). 25 years is a long time for Nintendo to be pumping out games of this quality on a regular basis, which is an impressive feat in and of itself.
Still, there was a 100% chance that Fi was annoying as hell.
A lot of people on the internet were angry when Wind Waker came out. I mean, "just watched an episode of the Zelda cartoon series"-levels of pissed, as many felt that Wind Waker was "too cartoony" for their tastes. They thought that Ocarina of Time was an indicator that as console graphics got more and more powerful the Zelda games would get more realistic and dark. So, in attempting to go in the complete opposite direction of Wind Waker, Nintendo answered with Twilight Princess.
Twilight Princess is (despite having most tween-sounding title of any Zelda game) probably the darkest Zelda game, in both the literal and figurative sense there's a lot of actual darkness in the game (as in "the absence of light"). Despite the commitment to realistic graphics and a darker storyline, the game was still recognizably Zelda through and through, with plenty of par-for-the-course weirdness like Link turning into a wolf and a strange being named Midna riding him and acting as a more personable Navi replacement.
It's also notable for being released for both the Gamecube and the Wii at the same time, since the Wii was in desperate need of decent launch titles at the time. Unfortunately, the game was developed with Link holding the sword in his left hand (since he's, ya know, always left-handed), which presented a problem for the Wii, since the vast majority of players would use their right hands with the Wiimote motion controls. Nintendo's decision of how to deal with this was to literally flip the entire game, as if you were playing it in a mirror. For a game series so devoted to puzzle-solving, it's hard not to be impressed by such a stupidly brilliant solution.