I have had a long history with Nintendo. The very first game console I have any recollection playing was the SNES when I was 6-8. Ever since then, my tastes may have changed (very debateably my skills have as well) and while I am now usually a JRPG/VN kind of guy, there has been many Nintendo franchises or games that I still cherish greatly. I am gonna talk about my favourite series and particularly my favourite games in those series. I also will mention my favourite Nintendo Consoles, since I don't see others posting about it yet and was curious what all your guys was.
Legend of Zelda:
They often say that your first Zelda game you beat is much like the first Final Fantasy you beat in that it's likely to be your favourite of all time. And despite it not being the first Zelda game I have played, Twilight Princes was the first Zelda game I played (and really only since I tend to play a lot of them and never finish) is my favourite Zelda game ever. The gameplay, while not as tight as Link to the Past, was generally great and what really drew me in was the characters. Midna is still my favourite Zelda character ever and her character arc is still the best and strongest in my opinion from a character in any Zelda game. The art style is also beautiful and I particularly the character designs. It did have some issues, like a brightness issue (making the game blacker than a Spinal Tap album cover) and an overworld that was a bit empty at times. However, I feel it also had some consistently good dungeons and the only Water Temple that doesn't make me question why I ever played these games in the first place. Lastly, the music I felt was some of the best (if not the best) in the entire series, particularly the hugely overlooked credits theme.
LoZ Game Order (ones I have played): Twilight Princess > Link To The Past > Majora's Mask > Ocarina of Time > Link Between Worlds > Wind Waker > Four Swords (on 3DS) > Legend of Zelda > Legend of Zelda 2
Mario (2D/3D platformers, specifically):
Hard to find anyone nowadays who hasn't either played a game from this series or at least has heard of it. Anyway, Mario games were some of my very first gaming experiences and for 2D Mario games, Mario 3 is my favourite. It felt like it had plenty of World variation rather than just changing seasons/weather and had some huge mainstays for the series (the overworld map, for example or the Mushroom houses). The platforming controls are also very tight and responsive and I felt this one was always the most fun to play. Super Mario World never clicked for me, but I also do love to go back to the first game on the NES. Super Mario Bro's on the DS was also fantastic, being probably my second favourite 2D Mario platformer. As for 3D, well I haven't played a lot of them, but I remember really enjoying Super Mario Sunshine, Super Mario 3D World and a DS port of Super Mario World 64.
As a side note, I did want to mention at least one of the RPG's and since I have only played two, I will say that Thousand Year Door is amazing and easily my favourite Mario RPG of all time (for now).
Super Smash Bros:
Classic nostalgia with this one. My introduction and favourite game in the series is Melee, since I spent hundreds of hours on it battling bots on the highest difficult settings and maining with Link and Marth. In general, I usually win most matches I play with my friends, but I never bothered with a competitive circuit (and haven't played in years so I am probably pretty bad at it now). I am far too casual when it comes to most games and especially nowadays, time may not be feasible to pursue competitive circuits. Regardless, Brawl happened and I think it was a step down, especially since the game only got more broken instead of less. Now that Smash on the Wii U and 3DS has been out for a while, I would say overall that its probably the best game out of all of them in terms of features, graphics and content, but Melee will always be my favourite.
This used to be (and still is) a childhood favourite. While I think the games went downhill after 7, I have played the ones on Gamecube (6 and 7), a DS Mario Party game (barely played it tho), Mario Party 8 on the Wii briefly and while I haven't played as many of them as I have other Mario games, I have had a lot of fun. However, I do standby the fact that this game will ruin friendships on an even greater level than Mario Kart, as there is an even greater element of chance involved in these games; this is especially true in earlier ones in the series. Mario Party 6 is my current favourite, though 7 and 8 were pretty good.
This is one that I go way back to Super Mario Kart on the SNES. I have played most of the Mario Karts at some point, though I don't think I ever played the DS version or NES Mario Kart. Though I largely played these games alone, I still remember having a lot of fun with them. Recently, I got fairly decent at Mario Kart 8, though sometimes I like to maintain that illusion by just playing with friends when they do occasionally come over.
Order of my favourite Mario Kart games: Mario Kart Double Dash > Mario Kart 8 > Mario Kart 64 > Super Mario Kart > the rest (haven't played the others)
One of the very first handheld games I ever played (on a GBA that had so much screenglare it was hard to ever see anything) was my copy of Firered. I lost it and the Leafgreen copy I believe I got afterward, but where I really fell in love was getting Emerald. There is certainly a lot of childhood nostalgia that I hold for that game and I have played a good number of them, only missing the original Gen 1 and 2 (played the previously mentioned Firered/Leafgreen and Soulsilver) and Gen 5 (lost interest around that time). Still, I remember the long periods of time spent stealing money after beating up Pokemon Trainers's Pokes who are far younger than me (and all the reminders about how good Joey's Rattata is). I also played a little outside of the main series by playing Collesium for a bit and Pokemon Ranger. Good games, though I either lost them or they didn't hold my attention for that long. Other remakes I played was Alpha Sapphire, which I loved despite the fact that I felt the credits theme wasn't nearly as good, though the original credits theme is my favourite Pokemon song of all time.
My favourite Gen's/Poke game order (lumped in the remakes to the Gen's they were updating)): Gen 3 (R/S/E/AS/OR) > Gen 2 (G/S/C/HG/SS) > Gen 6 (X/Y) > Gen 1 (R/B/Y/LG/FR) > Gen 4 (D/Pe/Pl)
(I never played Pokemon Moon or Sun nor Black & White or the sequel).
Donkey Kong (any Donkey Kong related game, really):
Donkey Kong Country and its two sequels are still games I very fondly remember playing in my childhood. The graphics were incredible for their time and the music is, in my opinion, some of the best ever composed in gaming ever. While I was never really good at the games themselves, the atmosphere, attention to detail and the gameplay were all perfect. I know most people agree that DKC 2 is the best but I think DKC 3 is underrated, despite the fact that I'd say it isn't as good as DKC 1 or 2. Donkey Kong Returns was decent, but I wasn't really blown away by another game in the series until I tried Tropical Freeze. I played it at a friends house and loved it. Definitely need to invest in a copy once my wallet is occupied by more than just flies and cobwebs. I also really enjoyed Donkey Kong 64 as a kid, though I reckon that most of that is nostalgia talking.
I have played a few games starring Wario, and they were generally really fun. My favourite is still Warioworld for the Gamecube, but Master of Disguise was cool. I never played a lot of these, but I did enjoy the couple I did play, so I thought I'd mention it since most people don't talk about them when talking Nintendo IP's.
Nintendo games/series I wanna play: Breath of the Wild, Mother series (especially Mother 3), Fire Emblem: Echoes, Mario Kart 8 Deluxe, Super Mario Galaxy (and the sequel).
Here are my personal favourite Nintendo Consoles (including handhelds):
Gamecube > SNES > 3DS > DS > GBA SP > N64 > NES > Wii U > Wii > Gameboy Colour > GBA (has no Switch, so I can't judge that one nor the original Gameboy).