There was a Zelda animated series, and it was terrible. Let's not dwell on it. But if you ever wondered what would happen if the same art style ditched the excuuuuuuuuuuuse me's and played things a little straighter, read on, because such a thing exists.
Actually, twelve of them do, in the form of The Legend of Zelda comic series, released in 1990 by Valiant.
Beginning in February and running for six issues, each comic contained two individual stories, along with one or two shorter, lighter pieces.
I say lighter because the primary plotlines, while using the art style of the ill-fated animated series, were actually much closer to the more serious tones found in the Zelda games of the time. The world is in peril, bad things happen, and there's even a two-part run where Link is consumed and corrupted by the Triforce of Power, to the point where he begins to resemble Ganon, pig face and all.
These stories were hardly epic tales. Cramming two of them into a single issue comic means they only ran around ten pages each. And it wasn't all making amends for the cartoon series, as the "bonus" comics included in each issue were often lighter in tone, like the one where Link and Zelda go on a date. Sigh.
Serious Zelda fans may also appreciate (or loathe) the lengths the comics went to flesh out the Zelda universe. Long before Ocarina, Majora's Mask, Wind Waker, Twilight Princess and Skyward Sword took Link to wild and vividly different places, these comics were dreaming up new kingdoms and worlds to explore. They even tried their hand at providing a little canonical back story, introducing the world of Calatia, a neighbouring Kingdom where Link and his parents Arn and Medilia came from.
The comics were written by George Caragonne, a man whose association with Nintendo comics would set him on a path to a tragic and untimely end. Having got his start in the business dabbling on licensed properties like GI Joe and Thundercats, he went on to pen many of Valiant's line of Nintendo comics (he even helped establish the company). Yet he didn't stick around long. Caragonne soon left to start up a new label with...Penthouse magazine.
After a few years writing there, first for the magazine and then for its spin-off comics label (in which he surprisingly found a great deal of success), Caragonne was fired for "financial impropriety". Accounts suggest that the success of Penthouse's comics had led him to a life of heavy partying and drug use, and it was alleged he'd begun stealing money from his bosses to help support his new lifestyle.
Shortly after he was fired, and with neighbours saying he'd become upset that "associates had stolen an idea he had for a comic book", Caragonne took a lift up to the 45th floor of the Marriott Marquis in Times Square, put on a Walkman (the James Bond theme, apparently) and leapt 500 feet to his death.
You can read way more about these comics, and see images of their contents, at the Zelda Wiki.