I've been to all of the home playoff games and home clinchers in this century. Other than those, road games stick out the most, partly because I try to get great seats.
2004 and 2005 clinchers in Oakland.
Peter Bourjos' first major league home run and Jordan Walden's debut in Minnesota (2nd row Angels dugout seats). Target Field's first year.
Angels (and my) first trip to Wrigley Field.
Angels 2008 trip to brand new Nationals Park (2nd row aisle seats behind home plate) and Citizens Bank Park (Angels went 4-0). Ran into Juan Rivera at the airport before the series was over and asked if he'd been traded.
Colorado 2012 - Long time coming. Saw one game with a bunch of family. Watched the first period of the Kings Stanley Cup clincher on the return flight home.
Kansas City 2012 - Terrorist, giant Mike Trout heads, and a Southwest voucher. Bugged Mark Gubica and Victor Rojas at the airport.
Others:
2010 Home Run Derby
2006 21-6 win against KC. DaVanon hit for the cycle. Jose Molina hit a grand slam.
2003 spring training vs Giants at Scottsdale. Angels fans were walking the concourse taunting Giants fans.
2002 Troy Glaus three home run game
2002 spring training brawl against the Padres