The first time I really got into gaming was with the 360, back in late 2009 during my Freshman year of High School. Growing up, I had always played video games, I had a PSone (with the badass travel screen) a PS2, a DS and a GBA at one point or another, but I was never into the media surrounding them. I had no clue when anything was coming out, I just played what ever looked cool up until that point. There were two incidents that changed how I looked at games and led to me buying a 360.
First, back in the summer of 2008 I played KOTOR (PC) for the first time. It taught me to love story based games and, to this day, I still consider my first playthorugh of that game to be one of my favorite experiences with games.
The second happened in 2009. My group of friends all started talking one day and our conversation eventually came around to the original Halo. I had never played it, but some of my friends had and they loved it. I eventually found the PC port for like 10 bucks at walmart, and it actually ran on the family computer (sub 30 FPS mind you, but whatever, it was still somewhat playable). I fell in love with it. I had played other FPS, but my experience was pretty much limited to the countless Medal of Honor games that were on the PS2. This was completely new to me. enemies with actual AI, huge levels, an engrossing story.
Around the beginning of the winter we all agreed to buy 360s. And thats when everything changed, I started paying attention to games media online (both of the traditional and youtube varieties), and my group of friend and I fell in deep with Halo 3 (like holy shit, I must have spent at the very least 100 hours in custom games alone). Past playing halo with friends, I had an entire library of games from 2005-9 to play through. Fallout 3 and Oblivion were an absolute joy to experience, Mass Effect was like reuniting with KOTOR again (and I rushed out day one to buy ME2), I got embarrassingly deep into CoD, Bioshock was a hell of a ride, and Dragon Age Origins became my favorite RPG of all time. There are a million others Im sure I'm forgetting, and thats not even counting everything that came out after, like New Vegas, Dark Souls, Skyrim, red dead and another million more.
My gaming tastes were really built during that time, and for that, the 360 will always have a place to me.