Mario: First game was Super Mario World. My first memory of Mario was watching my dad play Super Mario Bros. 3 at like 1 AM, unbeknownst to him. He was fighting Wendy O. Koopa - it's actually one of my earliest memories. I've played basically all of the mainline stuff and most of the spin-off stuff (what's worth playing, anyway).
Zelda: First game was A Link to the Past. I vividly remember getting literally all stuff I could (or thought that I could) - Ice Rod, Heart Pieces, Bottles, Bombs, Boomerang, Lantern, etc. - and then never beating the Eastern Palace for a long time because I was afraid of the orbs that launched down the narrow hallway when you entered. I've since obviously grown more accustomed to it, and I've played and beaten most Zelda games. The only ones I haven't beaten are Zelda II, Twilight Princess, Skyward Sword, and Spirit Tracks.
Metroid: Started playing Metroid when I traded a game for Metroid II, Dr. Mario, and Kirby's Dream Land. I enjoyed it, and then a while later my mom bought me Super Metroid at a rummage sale for a dollar, and that too was pretty fun. I eventually went on to get most of the Metroid titles, though I haven't beaten a lot of them. I'm planning on finally getting around to beating Prime.
Donkey Kong: Oddly enough, I never got super into the DKC series. I didn't grow up in the arcade era so the original DK games were lost on me, and the gameplay of DKC never clicked with me. They were good, no doubt about that, but I don't have fond memories. Due to nostalgia, I probably think more fondly of DK64 than any of the DKC trilogy. The only DK game besides DK on GB (which I love) that I've beaten is Returns on 3DS.
Pokemon: I actually bought Pokémon Red about a year before I owned a Game Boy, but when I got the Game Boy, I discovered that I lost it. My dad thankfully bought me Pokémon Blue instead. I later found Red and traded it to my friend for a game I don't remember. I later bought Silver, which I enjoyed
a lot. After that, I took a break, and skipped past the Ruby and Sapphire generation. Got back into it with Diamond and Pearl, though Pokémon has never impressed me like it did with Silver.
Yoshi: First game was Yoshi's Story, which I enjoyed quite a bit. I recognized that it's flawed in a lot of ways, but at least they tried something new, unlike Yoshi's Island DS and New Island. I never really played YI on the SNES - I was aware of it, and played it some, but my first real playthrough was on GBA. Beat it and YS, but didn't beat DS or New Island.
StarFox: Another series that I'm kinda down on. Not that I dislike it - I own or have owned the Super NES, Nintendo 64, and DS games at one point or another - but for some reason it doesn't really click with me. Haven't found a Star Fox game that I love quite yet.
Kid Icarus: Didn't grow up with Kid Icarus, got into it on Wii Virtual Console. The first and only game I've beaten in the series is Uprising. I loved that game quite a bit, and it stands as my top title in the series. This shouldn't serve to discredit the original, of course.
Kirby: Been a big fan of the series ever since I was a wee child. My first experience w/ it was Kirby's Adventure, when my aunt and uncle rented it for my cousin and I. We took turns playing through levels, though he was better because he was older at the time. He beat the final boss while I watched, and I remember being one step away from falling asleep. I later got my own copy of Kirby's Dream Land, and then got Kirby Super Star (which stands as my favourite multi-player game on Super NES). I've bought most Kirby games since.
Fire Emblem: I got Fire Emblem around when it first released, but I found it too hard at the time. Skipped SS, PoR, and RD, but got SS later. Bought Awakening, it was the first FE game I'd ever beaten. I plan on going back and finishing the two GBA Fire Emblems soon.
Punch Out!!: First experience was renting Super Punch-Out!! on Super NES. I liked it quite a bit - I even managed to get to Mr. Sandman! He totally creamed me, though.

I later got Punch-Out!! on Wii VC, and bought Punch-Out!! for Wii (which is the only one I've beaten).
Wario: I started with Wario Land 3, though I was aware of Wario Land II. It stands as one of my favourite platform games ever. Bought Wario Land 4 right when it launched, and while I liked it a lot, I disliked the departure from 3's invincibility gimmick. Played and enjoyed the WarioWare series, but didn't like that Wario became defined by his WarioWare titles.
Earthbound: Own and beat the Super NES one about 15 times, favourite game of all time. Played Mother 3 at least a few times. Amazing game, but falls slightly short of the original.
Gyromite (ROB): My dad owned R.O.B., so I played it a bit, but I think I didn't get how it worked so I never made progress in it.
Ice Climber: My dad owned a lot of NES games, including this. It was at least okay.
Pikmin: Played all three of them. The GameCube was my first home console that I owned outright, and I had Luigi's Mansion, Super Smash Bros. Melee, Super Monkey Ball, and Pikmin. Got Pikmin 2 for my birthday years later and loved it.
Sonic: Didn't grow up with it - my first real Sonic title was Sonic Adventure 2. I got Sonic Mega Collection because I decided that I wanted to like the Sonic games, but it never clicked with me.
Metal Gear: I find stealth games too stressful, so I've not gotten into the 3D MGS titles. I did play and enjoy the GBC game, though.
Animal Crossing: Enjoyed the GC game and the 3DS game, but I disliked the Wii and DS games a bit.
Wii Fit: Bought and used both Wii Fit and U for a long time.
Xenoblade: Bought it, but I have yet to play it.
Mega Man: Didn't really grow up with Mega Man. That said, I've recently gotten into the classic Mega Man and X titles, and gotten really good at them. Beat Mega Man 2 and X, and almost there with 1 and 3.
Pac-Man: No arcade lifestyle, but I liked the original a lot. I really, really loved Championship Edition DX, though.
Duck Hunt: Parents had an NES, so it only stands to reason that I would have played it. I actually owned all three iterations of it.
F-Zero: Haven't played any of them super in depth yet, but I enjoyed what I played.
Game&Watch: Parents had a single Game & Watch system that I played off-and-on, and I enjoyed the Game & Watch Gallery games.