2600: My dad bought one off a buddy of his back in the late 80s. It came with a bunch of games including the first game I ever remember playing, Joust.
NES: My dad bought this console so that he and my uncle could play through Super Mario Bros. 2. So that was the first game we got beside the Mario/Duck Hunt pack in
SMS: Once again this was a console my dad bought, got it with After Burner, Space Harrier, and Penguin land
SNES: Back in the late summer of 92 our local rental store just got an SNES available for rent. I convinced my mom to rent it for me as well as Turtles in Time. When my dad got home from work that evening and saw the console hooked up to the TV he asked me about it. I told him mom rented it for me. He tried the game I had rented and then went back to the rental place and rented Street Fighter II. Two weeks later I come home from school to see him and my little sister playing Street Fighter II on our new SNES. Worst part about that is that I literally got grounded two days before he bought the console
Genesis: First console that was actually purchased for just me. I got this back in 94 for my 10th birthday. Got it with Sonic 2 and Superman
Sega CD: Got this one for my 12th birthday. My parents were finally going to get me a Sega CD after years of bugging them for one. So we go to Toys 'R' Us to pick one up. Did I mention that my 12th birthday fell on September 29th 1996. Yep that's right the launch date of the Nintendo 64. So we go to the store and I see all the displays and I try out the new system. I beg my parents for one and they stick to their guns and buy me that Sega CD with a bunch of games like Sewer Shark, Tomcat Alley, and a bunch of other FMV games. So much better than a 64 with Mario 64. Oh well, now that I'm an adult I understand why they would rather get me the stuff on clearance rather than the shiny new thing
32X : Picked this one up a couple of months later on clearance at Toys 'R' Us
Saturn: Got this one for Christmas 96. With Vitura Fighter, Vitura cop, Sega Rally, and Daytona USA.
PlayStation: Got this one for my 14th birthday in 98. Got Final Fantasy VII and Wild Arms
Dreamcast: Got this in early 2000. Was at an auction with my mom and there was a lot that had a Dreamcast, Sonic Adventure, Shadowman, Powerstone, an extra controller and a vmu. There was a bunch of old people there that had no idea what it was I had my mom bid on it and got the whole lot for 90 bucks.
N64: Got this one in late 2000. Got it for a good price used from Blockbuster. Got both Ocarina of Time and Majora's Mask
PS2: My dad bought me this in exchange for helping him out at work. I got it in early 02 with GTA 3. I got it at a time where memory cards were hard to find and I didn't get one until like 2 months after I got the console. I got really familiar with the first mission of GTA 3.
Gamecube: First console I bought myself, got it used at EB games with Wind Waker and Resident Evil IV back in early 05
Xbox: Picked it up at a Gamestop back in 05 with KOTOR 1 and 2 as well as Jade Empire
Xbox 360: Back in mid 06 I had a full time job at the local Wal-Mart I was still living with my parents and had no bills so I blew an entire check on this and Dead Rising.
Wii: Got this one on launch with Red Steel and Twilight Princess.
PS3: Two weeks after launch I was walking through the electronics section after just picking up my paycheck, when I saw that we had a 20gb PS3 in stock. They also just informed me that because of the holiday we got double the normal employee discount on any one item. I knew it was meant to be and blew my whole check on the console and Resistance.
PS4: Got it at launch with Assassin's Creed IV.