The son of a jockey, Smith began riding races in his native New Mexico at age 11, and took out a jockey's license at age 16 in 1982. He left New Mexico the following year, riding mostly in the Midwest where he earned his apprenticeship at Canterbury Downs Minnesota before moving to New York in 1989.
In 1991, he became one of the few American jockeys to win a European classic by claiming victory in the Irish 2,000 Guineas aboard Fourstars Allstar (some other American jockeys, notably Steve Cauthen, had won European classics before Smith, but were based in Europe). The following year, he rode his first Breeders' Cup winner, Lure, in the Breeders' Cup Mile.
The year after that, 1993, he truly arrived as a top jockey, setting a North American record for stakes wins in a year with 62. Among his highlights were a win in the Preakness aboard Prairie Bayou and a successful defense of the Breeders' Cup Mile aboard Lure. That year, he won his first Eclipse Award for Outstanding Jockey, and also won an ESPY Award as top jockey. In 1994, he broke his own record for stakes wins with 68, 20 of them Grade I races. Several of those wins came while riding that year's Eclipse Award for Horse of the Year winner, Holy Bull. He also rode two winners in that year's Breeders' Cup, and again won the Eclipse Award as leading jockey. Smith went on to ride two Breeders' Cup winners in both 1995 and 1997.
In 1994, he was voted the Mike Venezia Memorial Award for "extraordinary sportsmanship and citizenship".
The dangers of Smith's profession became evident in 1998, when he suffered major injuries in two separate spills. A broken shoulder in March took him out of action for two months. Then, in August, while leading the Saratoga meeting, he broke two vertebrae in his back, requiring him to wear a body cast for several months. He came back six months after the fall.
In 2000, he moved his home base from New York to Southern California. That year he was voted the prestigious George Woolf Memorial Jockey Award that honors a rider whose career and personal conduct exemplifies the very best example of participants in the sport of thoroughbred racing.
In 2002, he had yet another banner year, serving as the regular rider for his second Horse of the Year, Azeri. He rode Azeri to a win in the Breeders' Cup Distaff, and also rode Vindication to a win in the Breeders' Cup Juvenile. Smith has ridden winners in 10 Breeders' Cup races to date.
In 2005, he rode 50–1 longshot Giacomo to victory in the Kentucky Derby. The win, Smith's first in the Derby, was something of a vindication for him. He was aboard Giacomo's sire Holy Bull, the 2–1 favorite in the 1994 Derby, but could only finish 12th after Holy Bull was bumped coming out of the starting gate.
Smith was inducted into the National Museum of Racing and Hall of Fame in 2003.