Um… I thought this is a topic that came up several times? No one outright asked "what's your favourite system", but I think I already have a rough idea on what each still-active member likes…
A little bit of disclosure for context: for GBA and older for handhelds and N64 and older for home consoles, I often get games through illicit means (Game Doctor SFIII, Doctor V64, downloaded ROMs), mostly because my parents and/or I didn't want to spend money (the "what do megacorporations lose from one fewer purchase?" mindset came to play). As such, the games I got for the older generations tend to have more variety, while I played safe on GameCube and early Wii, getting mostly what I knew for sure I would like.
I'd rank mine as such:
#1: Nintendo 3DS
I went into great length to
talk about this, but the gist is that there are multiple games that had me captivated, including Luigi's Mansion 2, The Legend of Zelda: A Link Between Worlds, Fire Emblem Awakening, Kirby Planet Robobot and many others.
#2: Nintendo Switch
This one is somewhat debatable. I have a large Switch library compared to other systems, but said library consists of games also available elsewhere on PC, other consoles and older Nintendo systems. Still, it's the Switch's versatility that convinced me to forego graphics and ease of data management to get games on the Switch over the rival consoles. And even on the merits of Switch exclusives alone, it's the home of excellent games like Luigi's Mansion 3 and Kirby Star Allies.
#3: Wii
It has Super Mario Galaxy 1 and 2, Kirby's Return to Dream Land and Fire Emblem: Radiant Dawn on it. It also plays GameCube games and gives us
the one update to Excitebike that I've really wanted. It's also the only Nintendo system to run Flash Player of any kind, even though it's a pretty bad implementation (Flash Lite 4, and it lags quite a lot).
#4: Game Boy Advance
It's hard to pick between #4 to #8, and if I'm asked again, I may arrange them differently. The Game Boy Advance gave me the first real taste of RPGs in Fire Emblem, Golden Sun, Mario Golf and Sting's Riviera: The Promised Land. The ports on the GBA tend to be inferior to the originals due to the system's lower resolution and sound developers not taking time to translate music to GBA properly, but games that originate on the GBA fit the system really well. It's also home to the WarioWare and Rhythm Heaven series, and I really like the former.
#5 Nintendo DS
Four Kirby games. And you know I love Kirby. (The 3DS has 9, but they consist of remakes and expanded sub-games.) Other than that, it's home to a large variety of games both touch-oriented and traditional, and sees the return of 2D Mario (which did get annoying later on, but at the time, there were no new 2D Mario in over a decade). It's also the first handheld to have an intuitive sleep mode (compare this to how GBA sleep mode works).
#6: Wii U
I made it pretty obvious that I like Super Mario 3D World and Tokyo Mirage Sessions ♯FE, and I also started playing Puyo Puyo on this system. I also enjoyed some of the other games like Paper Mario: Color Splash and Kirby and the Rainbow Curse, although those games have more obvious flaws. The Wii U is a case of not having many games I like, but the ones I do made me stick to them for a long time.
#7: Nintendo GameCube
The GameCube is home to fun games such as Mario Party 4, Mario Party 5, Mario Party 6 and Mario Party 7 (I don't have 5). Joking aside, the GameCube feels like a fun toy that I can do a lot of stuff with it: transfer games to a GBA, use mic input, and play unusual games like Super Mario Strikers (which also made people complain about modern Mario being "too safe") and Kirby Air Ride. I played the latter for a really long time, just for the scenic tracks and excellent music. It's also home to bug-fixed versions of Sonic Adventure 1 and 2, although I don't have those games.
#8: Super Famicom
I having fond memories playing the various versions of Super Bomberman (2-5) and Parodius (2-4) on it. There's also Super Mario World, although I was a primary schooler at the time, and neither my father (who did most of the playing back then, although now he mostly plays escape games on mobile, citing lowered dexterity) nor I couldn't get over Vanilla Dome back then. Also, Super Famicom had excellent music, particularly from the aforementioned Parodius, as well as Kirby Super Star, Fire Emblem: Genealogy of the Holy War and Sutte Hakkun.
#9: Game Boy / Game Boy Color
Starting from here, these are the systems I don't like as much as the others. In Game Boy's case, the low resolution is too low for most use cases. My favourite Game Boy games are the Game & Watch Gallery series. Besides that, I also like the GBC version of Mario Tennis. Most other games just don't work well, like Tetris and Puzzle League, where the Game Boy screen means fewer rows are in the play field than their respective standards.
#10: Nintendo 64
Nintendo 64 is where I can only find a few games I like. Super Mario 64, Mario Kart 64, Banjo-Kazooie (the first game), Kirby 64: The Crystal Shards, Super Smash Bros.… and not much else, really. Bomberman on N64 was no contest compared to his ventures on SFC and Saturn, and many other classic 2D games simply weren't on N64. Oh, it also started my long tradition of buying and subsequently disliking Star Fox. It hurts to see an IP with good potentials getting hurt by the difficulty every single time.
#11: Famicom / Famicom Disk System
Too low-tech for my taste. Screens are flashy due to imperfect screen refresh mechanism, music is often high-pitch and consist of 4 or fewer channels, which is really annoying, there's no save mechanism for earlier games (though this might be a blessing in disguise, since the save data depend on a battery), and whose brilliant idea is that a rectangle makes for a good controller? Anyway, my favourite game is Kirby's Adventure, while the other games I'm interested in all have better remakes on later systems.
Extra trivia: Puyo Puyo Tetris was the trigger point for me to get a Wii U (I was already wanting one for 3D World and ♯FE), and Fire Emblem Warriors got me to get a Switch (although I was already looking forward tko FE16 at the time). Both are multiplatform games that are also on (New) 3DS.