It's Tim Salmon. Normally I'd talk about other players who have worn a certain number or who's wearing it now, but for number 15 there's no point in doing so. The best player in Los Angeles Angels history to ever wear number 15 is Tim Salmon.
Tim Salmon is the best player to wear number 15 in Angels history.
Mr. Angel played his entire 14-year career with the Angels and wore number 15 the entire time. His career got off to an amazing start when he was the American League Rookie of the Year in 1993 after hitting 31 home runs and driving in 95 runs. Salmon would end up having four 30+ home run seasons with the Angels' two 100+ RBI seasons.
Salmon's best season came in 1995. He slashed .330/.429/.594 with 34 home runs and 105 RBI. Salmon was third in the league in batting, fifth in OPS, and seventh in bWAR. He was second in offensive WAR.
Salmon of course was a key piece in the 2002 World Series team. He hit third and came through when they needed him most. In the World Series, he recorded nine hits in 26 at-bats including two home runs and five RBI. He had a .908 OPS with four home runs in the 16 playoff games he played that season.
Unfortunately that was the only run he had in the postseason, but fortunately it ended in a victory.
Salmon ranks second in bWAR among position players in Angels history, second in games played, fourth in OPS, third in runs scored, second in hits, second in home runs, and second in RBI. Before Mike Trout came along he was arguably the best position player in the history of this franchise and remains one of the best.
Nobody has worn number 15 since Salmon retired in 2006, so it appears to be a matter of when, not if, number 15 will be officially retired for good.