[2] His pitching coach was Ray Knoblach, father of major leaguer Chuck Knoblauch.

[4] He is the all-time Rice leader with 20 career triples, and 2nd with 59 home runs, 243 RBIs, 499 total bases, and a .737 slugging percentage, trailing only Lance Berkman in each category.

Nevertheless, he still struggled to find significant time in the majors as the Dodgers favored Rickey Henderson in a reserve role over him.

Following a dozen at bats in Los Angeles, he was traded to the New York Yankees on July 31, 2003, along with Scott Proctor for Robin Ventura.

[6][7] Crosby played primarily as a starting outfielder (mostly in RF—where he has never made an error in the Major Leagues—and CF) for the Yankees.

In 2004, after having made the team due to a strong spring training performance in which he hit .385 with two home runs and eleven RBIs,[8] Crosby gained a large amount of media and fan attention when, in his first series against the Chicago White Sox, he hit two home runs with five RBI in first five at-bats and made a diving catch.

[9] Notably, the first home run came in his first at bat as a Yankee and the second secured Mike Mussina's 200th career win.

After having worked with Don Mattingly to shorten his swing, Crosby finished his 2005 season with the strongest performance of his career.

On September 19, 2005, in his first start of the year against a left-handed pitcher, he hit his career first walk-off home run, against Eric DuBose of the Baltimore Orioles, leading off the bottom of the 9th inning by sending a breaking ball over the right-center field fence.

With the Yankees up 2–1, the Angels had runners on first and second with two outs when Adam Kennedy hit a pitch off Mike Mussina deep into right-center.

Crosby and right-fielder Gary Sheffield collided while trying to catch the ball, allowing two runs to score and give the Angels a 3–2 lead.

Though he again made the team's opening roster, he lost almost a month on the 15 Day Disabled list from mid-May to June.