Great topic!
Launch Day
I was in college and went to the midnight launch at my local EB Games. We had a pretty tight gamer community in Tallahassee, so I knew a lot of the people in line, and was friends with all of the staff. It was just a really pleasant atmosphere. Local pizza shops caught wind of the event and brought pizza to sell by the slice to everyone standing in line.
Launch Games
I bought Madden, Perfect Dark Zero, Condemned, PGR3, and Call of Duty 2 at launch and enjoyed them all for what they were. Call of Duty 2 is still my favorite CoD, and Condemned really stands the test of time. Even though I knew greater games were still to come, the 360 launch lineup was more than enough to make me feel justified in my purchase of the system. Geometry Wars also helped a lot in that regard. I also still have my launch model.
Gears 1
Played all of them except for Judgement, but the first time I popped Gears 1 into my Xbox I was blown away.
Oblivion, Skyrim, Bioshock Trilogy, Mass Effect Trilogy
These games managed to pull me into a game world unlike any other games ever have. I was completely and totally invested in these game worlds. When I wasn't playing these games I'd be thinking about them, checking wikis and whatnot. I was obsessed with all of them.
Halo 3,Halo:Reach, ODST, Halo 4
I just really fucking love Halo.
RRoD and Japanese Xbox Support
I moved to Japan in 2006 and brought my US model 360 with me. Since then it has red ring'd twice and the Japanese support has been incredible. Both times they had it back to me within 5 actual days. The second time my 360 red ring'd it was the same week as the 3/11 earthquake and tsunami. The repair center is actually in Fukushima, which was hit hardest of all. And God bless 'em, they were open and fixing all 360s for free, even if you had an expired warranty. Incredible service, although I hear they no longer service US model 360s. I really hope that's not true, because I feel like I'm about to have my 3rd RRoD.