Summer: Atlanta 1996, Sydney 2000, Athens 2004, Beijing 2008, London 2012, Rio 2016
Winter: Lillehammer 1994, Nagano 1998, SLC 2002, Turin 2006, Vancouver 2010, Sochi 2014, Pyeongchang 2018
This set. First I remember was 2000, but I barely remember it. 2002 I remember because I saw the torch on its tour. 2004 I actually started following it, but don't remember any highlights. 2006 was the first one where the opening ceremonies really blew me away and that I'd say I followed very closely.
Apparently the 1996 bombing happened the same day my family went to visit a friend of mine a couple hours away, and I do actually vaguely remember that day, just not the bombing.