Winning the race is a moment of awesome for practically any rider.
Johnny Hoogerland was crashed into a barbed wire fence at about 40 km/h, and had to get 33 stitches in his legs. He still managed to complete the 2011 edition of the race. Badass. Video here.
Thomas Voeckler's way of riding in the 2011 edition.
Cavendish and Renshaw's victory on Champs Elysees in 2009. Renshaw was Cavendish' lead-out man, where he managed to finish second after the Brit. Champs Elysees is seen as the biggest sprinter stage the entire year. Video here, go to 3:40 for said sprint.
Filippo Simeoni's way of defying Armstrong's dominance in the peloton in 2004. Almost nothing good came of it, as he didn't quite have this skill to deal with the strong US Postal team. The one good thing was that Simeoni gave a big middle finger to a man who was a bit of a tyrant in the pack back in his days.
Michael Rasmussen defied Armstrong in 2005, but he did have the skill to back it up.
Pantani's record time at Alpe d'Huez, 37 minutes and 35 seconds, set in 1997. What's so awesome about that? In 2004, the climb up Alpe d'Huez was a time trial, which Armstrong won. Armstrong didn't beat Pantani's record though, being only one second slower.
The entire race in 2009 was one huge CMoA for Alberto Contador. He started out having a shared captaincy of his team with Armstrong, ending up obliterating all competition and showing Armstrong who was the boss.
Andy Schleck's stage victory at Galibier, attacking with 60 km to go and winning the stage by 2 minutes.
The actual plan was to have Andy attack, wear down the other GC-competitors trying to catch up, then have his brother and teammate Fränk counterattack and win this way. Plan didn't work out, but the Schleck brothers and their Leopard-Trek team were probably happy either way (Fränk finished second on that stage).
Stage 9 of the 2013 edition became a crowning stage of awesome. Attacks from the beginning by riders capable of doing stuff in the general classification, in order to wear down the Sky team, in a highly paced and exciting stage, where the plan somewhat succeeded (Froome got isolated, but stayed with the big guns). Stages like this is why cycling fans love the sport.