Love this thread!
I was born in '81, so my first experience with video games would have been the Atari 2600.
1.
Missile Command (Atari 2600)Simple, but highly addictive. My uncle purchased an Atari 2600 for us back in the early 80s and he brought two games with it, Missile Command and Pac Man. I didn't care much for Pac Man myself, but Missile Command was a lot of fun. I still remember the night we unpacked the Atari and spent the entire night taking turns with Missile Command; the adults were right in to it as well. We had played other games on the console of course, the best of which being River Raid, Smurfs, Vanguard, Frogger, Spiderman and Bowling. Nothing brings back fonder memories of the Atari though than Missile Command.
2.
Black Belt (Sega Master System)I could list so many games for this amazing system, but I want to go back to my absolute roots on the console, I can't look any further than Black Belt. My parents purchased a Sega Master System for us shortly after it's release as a total surprise. We were toothless (literally, I am pretty sure I was losing my teeth at the time), and we unboxed it early that Saturday morning.
This particular version of the console came with Hang On and Safari Hunt, as well as a hidden Maze game, which was all we played on it for quite a while. My parents did not have a lot of money, so we were just happy to have the console with a few games. My cousins on the other hand were pretty spoiled and they too got a Master System, but with quite a few games. My aunt was headed to the US for a shopping trip and before she left she came by with a Sega Master System catalogue and asked us to pick ANY game from it and she would bring it back for us. My brother and I scrolled through it and we agreed on Black Belt, it just looked so cool, and we loved martial arts, so it was an obvious choice for us.
She brought it back for us as promised and we played it endlessly. It was my first experience with any from the Hakuto No Ken series, though I didn't know it was Hakuto No Ken at the time, but I loved it. The boss fights where the sprites became much larger always got us excited. Struggling to beat ONI and RITA is also something I'll never forget. I still play through Black Belt often.
From there we did acquire a couple of other games, Shinobi and Rastan. To this day, the Sega Master System is right at the top of my list of most favorite consoles.
3.
Revenge of Shinobi (Sega Genesis)Our first experience on the Sega Genesis came in the form of Revenge of Shinobi, one of the early releases for the console. We had owned Shinobi on the Master System, so Revenge of Shinobi was something familiar to us, but man, the graphics were incredible! We were especially wowed by the appearance of Spiderman, Batman, Godzilla, and the Terminator. We loved everything about this game. We were definitely a Sega family.
4.
Search for the King (DOS)A bit of a deviation from console gaming for a moment, but Search for the King was an Adventure game that I couldn't put down. I was so intrigued by this game, along with Leisure Suit Larry, Space Quest, King's Quest and Police Quest. I had to settle on Search for the King though because it would be the game that first got me in to text/point-click type adventure games.
5.
Street Fighter II: Champion Edition (Arcade)This game basically took over my childhood. I would spend countless hours playing Street Fighter II at a local Laundromat that had this machine and Mortal Kombat. Mortal Kombat was fine, but I had always preferred Street Fighter II over it. Street Fighter II Turbo/Hyperfighting is my favorite Street Fighter II game, but Champion Edition is probably the game that really got me in to Street Fighter. I did often watch my brother play the original Street Fighter growing up, but I wasn't at an age were I could competently play it. When Street Fighter II came out though, I practiced and practiced and practiced, and to this day, I would consider myself to be a very very good Street Fighter 2 player. It wasn't until I started playing Street Fighter online through GGPO that I really blossomed as a player, but that's a story for another time.
6.
Street Fighter II - Turbo (SNES) I know I know, I've already mentioned Street Fighter, but it's a game that had to appear twice on my list. I never did own an SNES growing up, but my best friend did and I probably spent more money renting Street Fighter II - Turbo and taking it to his house to play than it would have cost me to buy the game three times over. We would spend hours and hours on weekends playing this game, never getting bored of it. I've got through many phases with street fighter, but I felt it was important to distinguish between the Arcade phase and then the console phase.
7.
Legacy of Kain - Blood Omen (PSX)My experience with the PS1 started when I participated in Mortal Kombat 3 tournament, but I didn't actually acquire the console until much later. I did however rent a PSX in order to practice for another tournament (Battle Arena Toshinden). That rental came with three games that I could include for the week, so I grabbed some game I can't even recall at this point and Blood Omen: Legacy of Kain. I knew nothing about the game, but it looked cool on the back of the case and the description seemed like something I would enjoy. I was not prepared for what was to come with this game. I didn't play the other two games. I didn't care much for Battle Arena Toshinden and the other game I rented sucked, so Blood Omen was it. Boy am I glad I got this, because the experience of playing through the game is one I will always remember. The story was so engaging, the characters were badass! Kain and Vorador in particular. It was the first game I had played on the PSX that made me want to purchase the console. I would eventually scrape together enough money to get one and play Soul Reaver when it came out.
8.
Phantasy Star - Sega Master SystemTaking a step backwards in evolution, but it was definitely one of the better gaming decisions I've made. At this point I had started my first part time job, and took up interest in collecting video games. Call me a collectard if you will, but I didn't chase after any and every game there was. I wanted to get those games that I had heard about growing up, but had never played or even saw. Rumor had it that there was a game called Phantasy Star on the Sega Master System that was as good as any RPG that had been released to date, and being a Sega Master System fan, I was a little surprised that I had never played it. As you can tell from my username, the only RPG I played on the Master System growing up was Miracle Warriors, and that game, while being really challenging (at least for me at the time), was apparently nothing compared to the mighty Phantasy Star. I managed to track a copy of the game down, which also happened to be my very first online purchase. I still remember going to the post office to get a money order to send to some person I had never met, in hopes they would send me Phantasy Star.
Weeks later, it arrived, and that game now holds a very special place in my heart. I spent the entire summer it seems playing through it. It was really really tough, and although it was being played on a console that had been all but forgotten by most, it was better than any game you could purchase at the time, at least in my books.
9.
Shenmue (Dreamcast)My list couldn't be complete without the Dreamcast being represented. Shenmue was the one game I probably spent the most time with on the console, and it was deserving of every minute of it. I felt like I was a professional fork lift driver after all was said and done, but aside from that, there was just SO much to do in the game. I especially loved all the throw backs to the Sega days of old in the game that I really appreciated as a Sega fan.
10.
Ninja Gaiden (XBOX)My brother purchased an Xbox for me while I was in University as a gift and got me Ninja Gaiden. We had actually played Ninja Gaiden quite a bit on the NES, and I was really excited for this title. In my opinion, Ninja Gaiden on the XBOX is as close to a perfect game as you can get it. If you haven't played it, you owe it to yourself to give it a shot.