Zach in Season 3 essentially winning the race single-handedly while carrying Flo, often literally at times. But then your head explodes when you remember that Flo just won the race too.
The Amazing Race anthology My Ox is Broken! even listed Zach as the Best Racer Ever for exactly these reasons.
Colin in Season 5 for setting up the Meta Game for the series.
Lena's unrolling of hay bales for eight hours straight in Season 6, never giving up until Phil had to come out just tell her and Kristy they had been eliminated. This ensured their place as one of the best-remembered early eliminated teams ever.
When Victoria accidentally cut her hand during the Mud the Hut Detour, she ran off to get water for her wound because mud got into it. Jonathan yelled at her for doing that (this is the same guy who shoved his wife because they lost a leg despite it being his fault) and Kendra, who has been a complete bitch for the whole season, is the first racer on the show to call him out on his horrible treatment of his wife as well as calling him an asshole in the process. He's had that coming for 9 legs and this is easily the best thing Kendra did for that season.
The Season 7 finale, particularly the last 20 minutes or so, with Uchenna & Joyce making an unbelievable comeback by first getting a pilot to pull back to the gate to let them onto the plane, then begging at the Finish Line to pay their cab driver. What followed was a Crowning Moment of Heartwarming.
Linda Weaver in Family Edition getting run over by a horse buggy - and getting back up. Say what you will about her - that looked painful!
Dustin & Kandice beating out the Fast Forward on leg 8 of Season 10, making them the first team to ever come from behind to win a leg in which a team won the Fast Forward (other teams have done it, but only because the team who won the Fast Forward was too far behind to win the leg... or else they sat around all day drinking tea). Made even better by the constant shots of the two teams who had taken the Fast Forward standing around, laughing about how miserable Dustin & Kandice must be doing an Intersection with one of the "weak" teams, turning the entire leg into one extended Description Cut.
Pulled off again in the third leg of the first season of TAR Latin America. Married couple Matias & Tamara (who had won the first two legs) were in the front of the pack and successfully took the Fast Forward. But in comes unathletic mother and daughter team Casilda & Casilda, who, despite being one of the last teams to leave the Roadblock, relied on their great navigational skills and won the leg, arriving less than 15 minutes before Matias & Tamara. Double awesome in that they took the faster Detour option that involved quite a tall zipline, which the height-fearing mother Casilda got through without batting an eye and not a second of complaining or hesitation, making it the second time she got through a height related task (the first being a rappell on the first leg) like she did those things on a daily basis.
Jet and Cord in Season 16 finishing in first place after they came in last on a non-elimination leg, even finishing the extra Speed Bump task in time to beat everyone else.
Claire in Season 17. After breaking a watermelon with her face, she keeps right on going with the task. Even better is that on her shot that hits the armor, the cameraman clearly wasn't expecting it to happen, and has to rush to get any footage of the armor falling over.
Nat and Kat, the first all-female winners of the US show in Season 17, after being firmly ahead during the entire final leg. Considering Kat's statement, "Tastes like a million dollars" on the same episode where Kat, a vegetarian, had to eat meat, and Nat had to face her fear of heights, this makes Nat and Kat's win all the more awesome and memorable.
In Unfinished Business, Kent and Vyxsin arrive at a U-Turn at the same time as Jaime and Cara, who pester them to give it to Flight Time and Big Easy. However, having learned their lesson from U-Turning a team that was ahead of them on their previous season, Kent and Vyxsin do it to the one team they know is behind them: Jaime and Cara!
The finale. For the first time since season 11, the team who wins manages to do so without having finished in first in any prior legs. Even their fellow racers didn't see that coming. My Greatest Second Chance indeed, Kisha and Jen!
In reference to Season 18, 3 teams who never got to show off their full potential in the race (Gary & Mallory, Zev & Justin, and Kisha & Jen), due to not lasting long enough or bad teamwork, returned to the race and ended up having the best 3 averages in the whole season and altogether winning 2/3 of the legs. They even outlasted all the teams in the season who made the Final 3 before (which was a total of 4), showing how strong they truly were.
Flight Time and Big Easy were U-turned in one of the legs. They not only quickly completed the second task, but caught up to and even passed some of the other teams, with the line "Double U-Turn that!"
Bill and Cathi's epic recovery. While they finished fifth overall, give them a bit of credit - typically, the race is biased against older contestants because while they have the teamwork, they lack the stamina or physical strength. Bill and Cathi finish in last on the very first leg of the race...but it was a non-elimination round. They then proceed to do very well in the race, being Overshadowed by Awesome by a couple team. They finished fifth overall, but for a team that almost was the first team eliminated, that's one big recovery, especially given their age and the fact that Season 19 was one of the harder races overall.
Before these two, let's give a hand to Meredith and Gretchen of Season 7. The fact that they finished fourth with Gretchen cutting her head in one leg and Meredith running several legs with a broken leg (something which production didn't even learn until after their elimination) was even more impressive.
Vanessa completing the roadblock in the penultimate leg of Season 20, which required her to run on a conveyor belt and grab rubber chickens hanging from the ceiling. The reason it's so awesome? She did it with a sprained ankle.
Season 21: Natalie & Nadiya's idea on how to use the U-Turn in a way it had never been used before. Taking advantage of Abbie & Ryan, a very strong team (and also poised to win 2 million dollars due to winning the first leg of this race), and being rather far behind most teams, the twins lay out the idea of the first team to arrive to the U-Turn to use it on Abbie & Ryan, and the team right behind them would in turn U-Turn the team who used it on Abbie & Ryan, effectively denying Abbie & Ryan the ability to use it on Josh & Brent, the only team behind them. While one of them was conflicted about using it, ultimately Jaymes & James U-Turned Abbie & Ryan, followed by Trey & Lexi U-Turning the boys, which pretty much led right to Abbie & Ryan's elimination, making the strategic idea on how to use the U-Turn work to perfection.
Brent and Josh themselves. They're easily one of the unluckiest teams to play the race...but at the same time, one of the luckiest. They survived two non-elimination legs and were consistently among the last teams to arrive at the pit stop, even entering the final leg being the last team to depart. Throughout the race, they kept getting unlucky streaks that should have normally eliminated them, but at the same time, they were lucky enough to manage to bounce back, either via a team sparing them with the U-Turn, James and Abba losing their passports, and other incidents. The other three teams left in the final four are pretty much in an alliance against them. Not only do they beat out Natalie and Nadiya, but they arrive first at the final leg, being one of the few teams to win the race without having ever won a previous leg.
In Season 22, Dave and Conner placed first in not one, but two legs after the former tore his Achilles tendon.
The second Botswana leg. Max & Katie and Joey & Meghan survived despite huge deficits. For Max & Katie, they couldn't find their car, got pulled over and had to complete a Speed Bump. For Joey & Meghan, they got horribly lost. Despite all of that, they survived the leg, beating out fan favorites Pam & Winnie.
Season 23: After 3 legs of Marie bribing teams with the Express Pass to get help from them, she and Tim get lost on their way to the Pit Stop. Nicole (from Nicole & Travis) turns the tables and tells them if they give her and Travis the Express Pass, they'll take them to the Pit Stop. They agree, and in the very next leg, Tim and Marie use their Pass after their cab driver had gotten them lost. This left Nicole and Travis holding the only Express Pass afterward, and in a very close third place position to start the next leg from.
Tim had his name cheered on by the eliminated teams at the Finish Line for putting up with Marie for the entire Race, let alone taking everything in stride and constantly wisecracking along the way.
Season 24: The marching band performing TAR theme song. That is all.
Leg 2: Seven teams arrived at the mat nearly at the same time. This is one of the rare moments that you'll see this many teams arriving onto the mat.
Leg 5: Despite leaving in last place (after being non-eliminated), and not being able to secure the flight the other teams were on, Brendon & Rachel made an incredibly risky move by taking a flight to Sri Lanka with a 30-minute connection, as many teams have tried similar gambits with longer connection times that still left them unable to make their flights. But they made the flight and went from last to first place with over an hour lead on the other teams. This was negated by a bunching point, however.
The Finale. Both Roadblocks are awesome: the first was an magic act assisted by David Copperfield, the second was a parachute jump which allowed the racer to land onto the finish line.
Props to Eric (9, 11) and Brendon & Rachel (20, 24), for finishing the race twice.
Amy and Maya - While not nearly as unlucky as Josh and Brent, they managed to finish the race when the editing was pointing towards the Soul Surfers as the obvious winners.
Season 28: In Leg 4, the record for the largest number of teams to arrive at the Pit Stop mat at the same time is broken by EIGHT teams.
Zabrina and Joe Jer from Season 1 of The Amazing Race Asia became the first all-female team to win any version of the race, something the original version didn't see until Season 17. Made more awesome by the fact that they never won a leg, were one of the non-athletic teams in that season, never used a Yield or Fast Forward, and in the final leg, surged from third to first place while facing off against two decent teams.
Marc & Rovilson's run in Season 2 of The Amazing Race Asia, where they ended up having the best season-finishing average in the race's history.
In Season 1 of The Amazing Race Australia, Sam & Renae enter the penultimate leg at a huge disadvantage: not only were they the only females left in a race where brute strength is rewarded over all, but they had also been "Marked for Elimination", which is nigh unbeatable without a Fast Forward, as seen in every other version to use it. In addition, there were several equalizers on the leg, which clumped every team together and robbed them of their previous time advantage. Any other team would have been pulverised - instead, they breezed through the final part of the leg at an unfathomable speed, checked in first to the mat despite another penalty they got for accidentally taking a private coach instead of a taxi, defeated every other team on that leg in spite of that penalty, and became the only team in the entire Amazing Race series to beat the previously unbeatable "Marked for Elimination" penalty. And a female team at that!
Overlapping somewhat with Heartwarming, TAR Australia 2 showed cops Shane & Andrew giving a child a little kangaroo toy after his grandfather helped them out during a task. What turns it into Awesome is when you look closely at the cops' bags and you see that they've bought along a whole bag of kangaroo toys. Why? They ended up giving the toys out along the way to every kid who helped them out during the race in tasks.
In the first Amazing Race Canada season, Tim Sr. managed to finish the final memory task with only 2 tries, even though most teams take more than an hour during such tasks, all despite having Parkinson's disease and the task being more complicated than usual since the teams had to remember Canada's provincial flags and flowers (which the Pit Stop Greeters wore). He singlehandedly led him and Tim Jr. to become the first parent/child team winners in the entire franchise, and he credits his wife for reminding him to pay attention as a challenge like this would come up.
Natalie & Meaghan dominating TAR Canada 2, and Mickey & Pete for defeating them. Sure, they had the theoretical advantage of being gold medalists in Winter Olympics women's hockey, but they transcended their already renowned reputation with their well-rounded prowess in physical, mental, and navigational skills (ironically doing their worst at the hockey task) and won over new fans with their positive attitudes. With 7 leg wins and one of the highest leg placement averages in the entire franchise, they were not just seen as arguably the strongest female team, but one of the strongest teams, period. Although Mickey & Pete were middle-of-the-road for most of the race, they knew they had to be perfect to win over the hockey girls, and it showed in their near-flawless final leg.
Even though they didn't win, you've got to hand it to Brent & Sean of TAR Canada 3 for managing to be good at many of the tasks and finishing first place in a good number of the legs. They were able to beat the more physically fit Gino & Jesse and Nick & Matt teams in some challenges such as the Curling Face-Off and the Waterskiing Challenge as well as completing the Needle In A Haystack Challenge faster than both teams. They probably could have won if they had pulled ahead, but even so, Brent & Sean did well for a team that had been underestimated during the whole race by the viewers and other teams. They were also the Plucky Comic Relief team since Sean vomit every time he pushes himself or gets anxious.