Well it might be a pretty long read but here goes
SNES
My sister owned a SNES, and as she says ever since I was about 6 months old I loved to watch her play it. She owned Super Mario World, Super Mario All Stars, A Link to the Past, and all the Donkey Kong Country games. My most recent memory is the day I turned 3, I played Mario World with her. We would play it all the time when she got home from school, my mom liked to play Link to the Past while she was gone. I never played it when I was younger though, I said it looked too hard so I enjoyed watching her play it. One day I spent the night over my grandpas house, and my cousin was over who also had an SNES. She liked Super Mario RPG, so she played that. When we had to leave my dad helped me get all my things, but I guess he figured that all the SNES games were mine because the next day I found Mario RPG in my bag. I never got the chance to give it back to her, as that was my last day seeing her. I do love that game though.
Nintendo 64
Me and my mom were walking around the store, we noticed they had a deal going on for N64 where you get 2 free games if you buy one. She knew I wanted to get one. So I got Mario 64 and Mario Kart 64 for free, and she bought a second controller. We got home and played Mario Kart for a few hours, it was a good time. On my 4th birthday my uncle got me Ocarina of Time, which I was amazed by at first sight because it was the first game I've ever seen with a gold cartridge. Knowing her love for A Link to the Past, I knew my mom would love this game more than me so I let her play it first. I sucked at Legend of Zelda, so I still just watched her play it. I also learned how to read from it, as she would read everything the characters said. Her and I had a lot of fun playing through it, and we still love the game to death. When Majoras Mask came out, we did the same thing. I got other games I love for it too, Spiderman, Goldeneye, Star Fox 64, Kirby 64, Banjo Kazooie, Banjo Tooie, Donkey Kong 64, and Paper Mario are the ones I remember most.
Gamecube
My Grandma got me one of these for Christmas in 2001, with Luigi's Mansion. I love that game, and it's part of the reason why Luigi is my and my Grandmas favorite Mario character. Around this time I met a new friend who had a N64, Gamecube, and PS2. We didn't play the N64 that much, and I'll get to the PS2 part later. I would go over his house pretty much everyday, and we'd play Super Smash Bros Melee to no end. Like seriously, it was practically a daily routine to play it for at least 3 hours. Probably wasn't good for us, but it was worth it. Then came the day my mom got the Zelda CE disk, I finally started to play the series for my own. The Wind Waker demo, and Zelda 1-2 were cool, but I played OoT and MM all the time. One of my previous "friends" borrowed it and moved away with it...so I haven't seen it since 2005 or so. We actually had to buy another gamecube around 2004, I guess my old one overheated or something. We still don't know what happened to it. When I got a new one I was so glad my old memory card still worked, and got Paper Mario The Thousand Year Door with it. Another game I just loved and played all the time. When Twilight Princess came out we couldn't afford a Wii, so we just waited a month for the GC version. And I don't regret it, I own both versions now and I prefer the GC version anyday. I'm not sure I appreciated it as much back then, but looking at it now I feel a lot more nostalgic for OoT and MM, but I have to say Twilight Princess is my favorite game now. Some people hate it, I personally love it to death. That, and Luigi's Mansion are my favorite GC games. Some others I got were: Spiderman 1, Spiderman 2, Super Mario Sunshine, Pikmin 1, Pikmin 2, Metroid Prime, Metroid Prime 2, Wind Waker, and Star Fox Assault.
Wii
I got one of these for my 12th birthday in 2007 with Super Paper Mario, which is the main reason why I wanted to get one because that's one of my favorite series. I wasn't very disappointed with it like others are, but I do admit it wasn't as fun as the first 2. We finally got internet service in 2008 just for it, but had no computer. I know, sounds weird. Having internet but no computer. So I downloaded a bunch of Virtual Console games, ones for I missed out on and ones for nostalgic purposes. I used the internet browser channel on it for youtube, and some other pages. I met some people over it and we traded Smash Brothers Brawl friend codes, they turned out to be the best friends I ever had and I still talk to them a lot. Most people say the Wii online service sucks, and to be fair yes it kind of does if you compare it to XBL or PSN. But it holds a special place in my heart because if it weren't for it, I wouldn't know the friends I have now. Everything else that came out for the Wii after that wasn't so great or memorable IMO, I mean I got the games for it and had fun with them while they lasted but after a month or so they just sat on the shelf. Even Skyward Sword, I wasn't really excited for it because I thought they were going to just dumb everything down like they have usually been doing lately. Of course me being a loyal Zelda fan I got it day one and was proven wrong, as it is a great game and no doubt at all in the best of Wii games. Not as great to me as the previous games in the series, but it delivered.
Handhelds
I don't have much of a history with handhelds so I'll just put them all here. My brothers owned a Gameboy color and their only games for it were Pokemon Red and Blue, so we took turns playing them on the go whenever we were out. Only game for it that I got was Pokemon Silver, which is still my favorite Pokemon game. I got a Gameboy Advance SP while it was on sale with Mario & Luigi Superstar Saga. That and the Minish Cap were the only games I had for it, but I didn't like the Minish Cap that much so I just continued to play Superstar Saga. I never owned any sort of DS for myself until the 3DS, as the games on them gave me little to no interest besides Mario & Luigi 2 and 3, so I just played those on a friends DS Lite. With the 3DS I got OoT3D which was nice to see with updated graphics, and the ability to play it wherever. Super Mario 3D Land and Mario Kart 7 were nice, but pretty short lived. More recently I tried out Kid Icarus: Uprising, but it's really another game I just don't see what's so great about. Downloaded games I missed out on, like Links Awakening and Kirbys Dream Land. I always thought the PSP had no good games besides the 2 God of War games it has, and the PS Vita is the same for me. Sony just does not interest me with Handhelds.
PS1
I never owned one of these, only games I liked for it was the Crash Bandicoot series. I played Spyro the Dragon as well, but I just don't see what's so great about it. But the startup sound for the system makes me feel pretty nostalgic. My brother would play Final Fantasy 7 on his, but again I just don't see what's so great about it.
PS2
I was never interested in one of these because I thought it would be the same as PS1 for me. My best friend had a PS2 with Sly Cooper 1&2, and those games alone made me want a PS2 for myself. When the third game came out Gamestop or Walmart had a deal you would get all 3 of them for free with a purchase of a PS2, so that's when I got one. Didn't own very many other games for it. But there was this Hulk game, Ultimate Destruction I believe it was called. It was awesome, pretty much GTA...with Hulk instead. Of course I didn't own any of the God of War games back then, because my mom didn't let me buy rated M games until I was 15 which I'm grateful for. I really like the series, but it's overrated IMO. Last thing I did with it was Star Wars Battlefront 2, and all I can say is I'm disappointed that the third was canceled.
PS3
I didn't even think about getting one of these until 2010 because you know...FIVE HUNDRED NINETY NINE U.S. DOLLORS. But one of my friends got one with Sonic 2006...Sonic games haven't been the same to us ever since, he traded it in a week later. When I got one I started to buy Blu Rays instead of DVDs because I don't buy movies that often anyway, so why not get the best quality for the ones I do buy. I enjoy most of the series on it, like Uncharted, Infamous, God of War, Killzone, etc. I'm not really waiting for much to come out for it at the moment, I'll just get whatever does and see how it is.
Xbox
I always hated this thing, the controller was ugly and the only thing it had was Halo 1 and 2.
Xbox 360
I turned out liking this system a lot more than I thought I would. When I got one I got Halo 3, Call of Duty: World at War, and Left 4 Dead. Playing a random Versus game of L4D I met someone who is now currently my best friend. Call of Duty World at War is in my opinion the best Call of Duty ever, second being Black Ops. I enjoyed the campaign the most out of them all, the multiplayer actually interested me, and zombies...I just love this mode so much. The storyline in it is great, and the maps are all fun to play. I still play Black Ops zombies a lot. While I do think that Call of Duty is no doubt the most overrated series of all time, I honestly can't wait for Black Ops 2. But again, only for zombies. Multiplayer and campaign from that series just don't interest me anymore. I really can't go into detail for every single game I've had such a great time with on this system, because that would take forever. One series I will note is Assassins Creed, this series to me is just amazing and I can't wait for 3.
PC
I pretty much only play Valve games on my computer...yeah that's it.
So yeah that's it, sorry about the mega post. Video games are practically a way of living for me