Definitely. The remastered graphics are absolutely stunning in 3D, and the game has a ton of content to keep you busy. Easily the best 3DS game available right now, and it's a great place to start if you're just getting into Zelda. I recommend giving it a shot, and if when you like fall in love with it, you'll also have The Legend of Zelda: Skyward Sword to look forward to soon (assuming you have a Wii, that is).
And you could also dip into other older Zelda games. The Legend of Zelda: Link's Awakening DX for Game Boy Color is great and it's available for only $5.99 on the Nintendo eShop. The Legend of Zelda, Zelda II: The Adventure of Link, The Legend of Zelda: A Link to the Past, the original The Legend of Zelda: Ocarina of Time, and The Legend of Zelda: Majora's Mask are all available on the Wii's Virtual Console, too.
Also worth playing if you can hunt them down are The Legend of Zelda: The Wind Waker (my personal favorite) and The Legend of Zelda: Four Swords Adventures for GameCube, and The Legend of Zelda: Phantom Hourglass and The Legend of Zelda: Spirit Tracks for Nintendo DS. And, of course, there's The Legend of Zelda: Twilight Princess, available for both GameCube and Wii. (You can get the Wii version for only $20 now as a Nintendo Select title, which is a steal for a Zelda game.)
Oh, and this September Nintendo is releasing a free DSiWare version of The Legend of Zelda: Four Swords, a fun little multiplayer Zelda game that originally came bundled with the Game Boy Advance remake of The Legend of Zelda: A Link to the Past.
And that pretty much covers all the main series Zelda games, except The Legend of Zelda: Oracle of Seasons, The Legend of Zelda: Oracle of Ages, and The Legend of Zelda: The Minish Cap. These three are going to be the hardest to find/play due to them being older games and not being available on Virtual Console at the moment. The Oracle games will probably be released on the eShop in time, but you'll probably need to hunt down a used copy of The Minish Cap if you want to play it, assuming you have the hardware to play it on (Game Boy Advance, or Nintendo DS/DS Lite).
Oh, and what Psychonaut said.