Larry, in cycling when a group finishes the whole group will get the time of the first cyclist. But if there is a gap the group becomes 2 group and the cyclists will get the time of the first cyclist in their group.
There is one exception to this. If some cyclists fall in the last kilometer of a race, the will get the time of the fastast cyclist in the group they were in during the fall, providing the will finish.
In multi-day stage events like the TdF you can win 'Bonafication seconds'. In the stages without maintains you can win those seconds, ie they are deducted from your time.
Those point can be during the stage (the first cyclist to pass gets 6 seconds, the second 4 and the third 2 seconds) but on the finish the give away up to 20 seconds for the first 3 cyclists.
There are 4 jurseys in the TdF:
1. Yellow: For the fastest cyclist overall
2. Green: For the best 'finisher' this year won by Erik Zabel (Germany) who won the 20th stage and had several second places. He has won it for the fifth time in a row, a new record.
3. Red spots: For the best climber, this year won by Botero (Columbia) who also won the 14th stage (in the Alps)
4. White: For the best Young cyclist. A young cyclist must not be older then 23 years and must not cycle professionally for longer than 2 years. Mon by Mancebo (Spain) who finished 9'th overall.

There are some extra prizes:
Best team: The time from the best 3 cyclists per team per stage added up. Won by Banesto (Spain)
Best attacking cyclist: Won by Erik Dekker (Netherlands) who has won 3 stages by escaping the great group. (1 time solo and 2 times with another cyclist) During the TdF he rode over 600 kilometers ahead of the great group. (1 stage has a average length around 200 km)

You are right that most TdF's are won in the mountains AND the individual time trials. But in the last 25 years the TdF is only won by 2 'pure' climbers.
Also a few years ago, 4 cyclists had escaped the great group in one of the early stages and finished 12 minutes before the favourites. One of them (Ciapucci) managed to follow them in the mountains and finished on the podium that year.

Also this year, Amstrong won 40 second of the second best (Ullrich) in the team time trials and thus giving a small moral blow, before finishing it off in Lourdes.

Regards,