2008 Summer Olympics (August 8-24)
Beijing 2008 (archived); Olympic.org; Wikipedia
Held in Beijing, China. The main thing I remember about this is that the opening ceremony was really great, and it's the first time I clearly remember taking a particular interest in an Olympic opening ceremony. Though that hardly seems likely; it's probably just that my memory sucks, as I might have mentioned. In fact, I don't remember anything specific about this year's ceremony, just the vague fact that it was great (and in subsequent Olympics, commentators continue to reference it as such). I don't remember anything specific about the games themselves, though I see Michael Phelps's name mentioned again, so it's as likely (if not more so) that I saw him compete here than that I did in 2004.
2010 Winter Olympics (February 12-28)
Olympic.org; Wikipedia
Held in Vancouver, Canada. I don't remember anything about this, and I'm not sure that I watched it at all. Looking for familiar names, I see Bode Miller, which sounds only very slightly familiarish, and Lindsey Vonn, which is perhaps slightly more familiar. And again, Shaun White (whom I must have first seen in 2006). So it's probably one of those years that I remember more for having heard about it in the news than for having actually seen any of the events.