I got into the series with both Ocarina of Time and Majora's Mask with the Collector's Disk on my GC. I had seen Link before in Smash Bros. 64 but didn't really know anything about him, and though I saw my brother play OoT with his friend on the N64 all I remember back then were the scary parts so I shied away. We had just gotten the GC with that disk included, and my brother, sister and I all started up separate files in OoT and MM. I would play OoT for a while, switch over to MM whenever I got bored of it, and visa versa. I finished MM only a day or so after OoT due to this mixed manner of playing.
While there is so much for me to enjoy about the series - Link himself, the whimsical charm, the creepy parts that rear their faces every now and again, the sense of adventure and heroism, the characters and how you get emotionally attached to them, etc. - what I really like most is the gameplay. Nothing else plays quite like it. I love the main sword & shield fighting style (the more realistic to swordplay it is, the more I'm attached to it), but I also love all the wacky side items Link also uses, the mind-bending puzzles and dungeons, the quasi-RPG method of upgrading gear & going out on quests, and the heart-pumping boss fights (the harder, the better).