Rod Carew was one of, if not the greatest hitter in Minnesota Twins history, having won the 1977 MVP and was an All-Star in all twelve of his seasons there.  The Twins traded him west to California in 1979, and while Carew was not clearly declining, he was still one sweet hitter.

Carew, who won six Batting Titles and four OBP Titles as a Twin, batted over .300 in his first five seasons in California, with all of those years showing an OBP over .380.  As an Angel, he collected his 3,000th Hit, and 968 of his career 3,053 Hits came on the West Coast.  Carew retired after the 1985 season, having batted .314 with the Angels.

The Angels inducted Carew into their Hall of Fame in 1992, a year after the Baseball Hall of Fame enshrined him on his first year of eligibility.

The Colorado Rockies drafted Chone Figgins, but before he made it to the Majors, he was traded to the Angels, which worked to his benefit.

Figgins made it to the bigs in 2002, playing a small role in the Angels' World Series Championship. Playing mainly at Third, Figgins was a regular starter in 2004, and through the rest of the decade, he was one of the top base-stealers in Baseball.  Figgins swiped at least 30 bases annually from 2004 to 2009 for the Angels, including a league-leading 62 in 2005.  He did not bring much power but did spray the ball often, collecting 1,045 Hits for the Halos, and was the league leader in Walks in 2009.  Figgins was an All-Star that year, the only time he would be, which was his final season in Los Angeles, as he left for Seattle as a Free Agent at season's end.

You didn't need a name or number on the back of Dean Chance’s jersey to know it was him who was pitching.  After obtaining the sign from his catcher, Chance rotated his body so that his back and head were looking towards second.  It worked for him, as one year, he was considered the best on the mound.

Chance debuted in the Majors in 1961 and made the starting rotation the following season, where he was third in Rookie of the Year voting with a respectable 14-10 record with a 2.96 ERA.  Chance slipped a bit in 1963, but he came back with a monster 1964, which was so good that it earned him not only a top-twenty rank on this list but the Cy Young Award.  The right-hander led the AL in Wins (20), ERA (1.65), Shutouts (11), Innings Pitched (278.1), ERA+ (200), and FIP (2.39), with a fifth-place finish in MVP voting.

Chance could not repeat what he did in 1964 but was still solid over the next two seasons before being traded to Minnesota.  With the Angels, Chance had 74 Wins against 66 Losses with a 2.83 ERA.  The organization inducted him into their Hall of Fame in 2015.

Dubbed "K-Rod," Francisco Rodriguez established himself as a top reliever when he was a rookie and barely one at that.  

Rodriguez was called up in September of 2002, and due to injuries, he was given a vital role in the Angels' postseason, where he had 11 appearances, won five Games, and had a sub 1.000 WHIP in all three of Anaheim’s series.  The Angels won the World Series, and it is hard to imagine this happening without Rodriguez.

Proving his performance was no fluke, Rodriguez was a set-up man in 2003 before moving to the closer's role in 2004.  K-Rod was an All-Star in 2004 and would lead the American League in Saves in both 2005 & 2006.   Rodriguez went back to the All-Star Game in 2007 and 2008, with the Venezuelan recording a then-record 62 Saves.  He won the 2006 and 2008 Rolaids Reliever of the Year, and he finished in the top four in Cy Young voting three times.  Rodriguez left the Halos after the 2008 Season for the New York Mets as a Free Agent.

As an Angel, Rodriguez compiled 208 Saves with a 2.35 ERA.