Sorry for the long post.
I originally played a bit of this game in 2001. I came right off of Ocarina of Time, which amazed me. I just couldn't get into it. I could not comprehend the concept of tension in the game, I couldn't stand the 3 day cycle thing because I felt it made the game restrictive...
But, I've been meaning to give it another shot for the longest.
So I obtained the Zelda Collectors Edition disc that contains 4 Zelda titles in it including Majora's. I mostly got it for Ocarina so I could replay that classic, but I still wanted to give Majora's another chance. So last night, after completing Castlevania and our election party was over I booted up Majora's Mask...
I didn't go to sleep until 2.

A few of my more recent complaints with the Zelda series has been:
1. The formula, they really need to expand upon the item -> dungeon -> item -> dungeon, rinse repeat formula. What's more, I hate how in Zelda games the only reason you ever visit the dungeons is to ALWAYS resurrect something or gain some power. Visit 3-4 dungeons and you can get the Master Sword! We've seen this in multiple games. It has become canned as hell. Your reasons for visiting dungeons is often so vapid in the games sometimes I wonder why I am in them. The formula in general has become stale.
Majora's Mask, however, places emphasis on sidequesting and exploration. When you actually go into a dungeon you feel as if you have an actual means for being there beyond gaining some new power or item. Despite coming out in 2000 Majora's Mask still feels fresh due to its unique 3 day formula. When you're in the middle of a dungeon on the final day and you finally make that boss succumb, it feels so rewarding. The tension really adds to the game, and what's more, makes you prioritize actions more so than you normally would in a Zelda game. I've been playing it almost like how I would Dead Rising - placing priorities as I juggle what I want to do next or whether I want to do something at all because I don't have the time for it.
2. The stories are almost always the same. Link has to save the world, okay. Neat. Every time. But this time I actually care. His fairy friend is awesome and not annoying like Navi, the game is full of npcs with more personality than any Zelda game before or after it. Right now I'm trying to find some guy named Kafei. I have his mask, I know where he is, but I have no clue how to talk to him or make him take off that damn Pikachu mask. And that's Majora's Mask in a nutshell - almost every single action I'm doing is to satisfy my own curiosity to unravel the game's world piece by piece. The game doesn't rely on Zelda or Ganon either which gives MM bonus points.
3. The more recent games (TP, WW..as much as I like them) are entirely too simplistic. Every thing in MM, however, works because every thing has an inkling of depth to it. The pre-dungeons are in depth, the first dungeon was the deepest first dungeon I've seen in a Zelda game - it wasn't particularly complex but it was still more advanced than the average first dungeon in a Zelda title, the first boss was far annoying than the typical first Zelda boss which often stray too far on the easy side (either that or I was fighting him wrong), the sidequests are in depth requiring a tremendous amount of work and effort to see everything.
When beating the first dungeon, you're told the Deku Royal Family's butler has a surprise for you. I went to him expecting him to just give it to me, as is typical of Zelda games, but no - I had to chase him through a giant mini-dungeon in order to reach my reward; a task that took several retries before I could get there. In order to gain new powers you have to visit Fairy's but unlike other Zelda games where you simply have to go find where they are, in MM you have to seek out their body parts to restore them, and *then* get that ability or item you want. The game requires a level of commitment in order to rewarded far more than the typical action adventure game.
So far I've beaten the first dungeon only, but I've acquired a few songs and a few masks (Giant Fairy, Pig, Kufei, Animal / Eagle thing, Deku), a few abilities (like the ability to charge my sword up to orange). I'm trying to see everyone's daily routine and do a few sidequests before I continue on to the next dungeon.
This game rocks. I hope the next Zelda is like Majora's Mask. Seriously. This game contains pretty much every thing I've wanted from a Zelda. Hopefully it keeps this up.
Tips would be welcome!