1. The Legend of Zelda: Majora's Mask
Something I've noticed with Zelda games is that the less I like them initially, the more I grow to like them. Ocarina of Time I thought looked really lame at first, but when I saw my brother play it, I got hooked at it became my favourite game for the next 6-8 years.
Majora's Mask I couldn't really get into even after having played it myself. I don't know if the reason was the time mechanic or the worn out N64 controllers, but something was stopping me from really getting to enjoy the game until almost a decade later when I played on the Wii Virtual Console, and then it quickly became my favourite. I loved the setting, the world, the personal stories NPCs had... Mechanically it also did pretty much everything better than Ocarina of Time, and I was amazed I hadn't realized that when I had first played it as a 7-year-old.
2. Pokémon HeartGold/SoulSilver
Did everything Pokémon G/S/C did, but mostly better. I love the physical/special move split, it still has the best menus of the series, Kanto was a bit more fleshed out compared to the GBC originals. Just a fantastic game overall.
3. Pokémon Platinum
I didn't include Diamond and Pearl because I never played them, and I've heard that they had a lot of problems that were fixed in Platinum, like slow battle speed, and the variety of Pokémon available.
Anyway, this was the first Pokémon game I played with the physical/special split, and really like Sinnoh as a map. The game was also a huge upgrade from the GBA games.
4. Pokémon Gold/Silver/Crystal
These games are the finest example of a sequel done right. They improved everything about the first games; there are a lot less glitches and all the Pokémon all look like they do today both from the front and the back.
I really appreciate Team Rocket not being a bunch of lunatics like almost all future Pokémon villain teams. I adore the fact that the game is very much just a personal journey to become a Pokémon champion, and no legendaries are tied to the story, unlike in the remake and pretty much all future Pokémon games. You might play through the game without ever even getting a chance to capture a legendary Pokémon, and that makes them feel more valuable, and more worthy of the legendary title.
To fully appreciate the game, you reakkt should play this game on the GameBoy Color, not emulate it or play it on GBA or the GameBoy Player. Only the original hardware do the visuals and sound justice. It's a bit unfortunate that my own GBC's buttons are very worn out due to heavy use, but I still prefer playing these games on it over anything else.
5. Splatoon
This was a game I did not expect to get into. I just decided to test the game out when they did the initial Global Test-Fire session, and I ended up really liking the game. I did get bored of the game just about a week after release, but when I came back a few months later, I was just as hooked on it as I had been during the first few days of Splatoon, which has only happened with very few games. Kudos to the people who worked on the free game modes, weapons, etc. and kept the game fresh.
6. Paper Mario: The Thousand-Year Door
Best Mario game hands down. It's funny, it has interesting characters and places we've never seen before. I could not put this game down when I first played it. Chapter 2 is really dull on repeat playthroughs though.
7. Star Fox 64
My favourite shoot-'em-up. The first Sin & Punishment is a pretty close second, but playing SF64, or Lylat Wars as I prefer to call it, is just so jolly.
8. Super Mario World 2: Yoshi's Island
The greatest 2D platformer of all time. Lovely art style, great music and level design, and the egg making/throwing was fun. Never really found Baby Mario annoying like a lot of people do.
9. Banjo-Kazooie
Still one of the very few games to do 3D platforming better than Super Mario 64, which many say is the first game to do 3D platforming right. The game is also very funny.
I mostly prefer Kazooie over Tooie because of the stages. Kazooie's worlds were simple enough that they were never confusing to navigate, and I like most the themes used for the stages better. I enjoyed playing every single stage in Kazooie, but there were at least 3 stages in Tooie that I didn't much care for.
10. F-Zero GX
This game is so good! I never thought that I would like a racing game this much.
It's fast and intense, has a large roster of characters and vehicles, and most importantly, the game is very cheesy. The cutscenes in story mode and the interviews after GPs are just wonderful. The music is also pretty good, and I like that the game allows you to create your own vehicle.
Really the only things missing here are a course creator, X Cup equivalent that creates random tracks for you to race, and an online vs. mode. Take notes Nintendo.