It's both. There is a team winner and an individual winner. It is a team's job to aid its top rider – be it Lance Armstrong or Alberto Contador – in winning the whole Tour de France.
An individual must enter the Tour de France with a team, and in this increasingly competitive race it has become increasingly necessary to have strong supporting teammates.
There is both an individual winner and a team winner, both determined by overall time. A team time is the compiled time of a team's three fastest riders. There is a cash award in both categories, and often an individual winner splits his winnings with his team, too.
A team often has 20-odd riders, but the team manager chooses only nine to ride in the Tour. Most of them are paid handsomely for the less-flashy roles of carrying water bottles, shuttling between the team car and top riders, and leading the peloton to create a draft. These riders are called “domestiques” (French for “servant”).
Lance Armstrong surrounded himself with teammates specifically chosen to complement his riding abilities and increase his chances for winning a record seven Tours in a row from 1999 to 2005. Stellar teammates such as Floyd Landis sacrificed their own chance at winning in order to gain experience and prestige racing alongside Armstrong.
In 2009, however, Team Astana itself turned into a competition between teammates. Armstrong and teammate Alberto Contador were only two seconds apart at the midway point and less than 10 seconds off the leader. Contador would go on win, with Armstrong accusing him of failing to support the team.
This year, the rivals are competing on opposing teams, with Armstrong for Team RadioShack and Contador still for Astana.
The first Tour was in 1903, and for its first three decades was comprised of unaffiliated racers alongside trade team racers. Both were barred from the race for the following three decades and only regional and national teams competed until the 1960s, when trade teams were again allowed to compete.
This year, the world’s 16 top-ranked teams were invited to the Tour, with the remainder chosen by wild card, in compliance with the agreement passed with the International Cycling Union in September 2008. Starting in 2011, the 17 top-ranked teams will be automatically selected with the other teams selected by wild card.