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.
Lena's Determinator unrolling of hay bales for eight hours in Season 6, never giving up until Phil had to come out and tell her and Kristy they were eliminated. Ensuring their place as one of the best remembered early eliminated teams ever.
When Victoria accidentally cut her hand on the Mud the Hut Detour. She ran to get water for her wound (mud got into it) and Jonathan yelled at her for it. (This is the same guy who shoved his wife because they lost a leg despite it being his fault) Kendra,(who has been a complete bitch the whole season) is the first racer on the show to call him out on his horrible treatment of his wife, calling him an asshole in the process. He's had that coming for 9 legs and that is easily the best thing Kendra did in 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 on 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 them - that looked painful!
Dustin & Kandice beating out the Fast Forward on leg 8 of Season 10, making them the only 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 come unathletic mother and daughter Casilda & Casilda, who despite being one of the last teams to leave the Roadblock, relied on 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, and 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.
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! And then it gets better: it's a double U-Turn, so Jaime and Cara go ahead and give the other one to Flight Time and Big Easy, only to be passed by them anyway and finish in last place.
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 having the best 3 averages in the whole season and all together winning 2/3 of the legs. Even outlasting all the teams in the season who made the Final 3 before (which was a total of 4) showing how strong they truly were
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 double the normal million-dollar prize due to winning the first leg of this race), 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 others. 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 in first at the final leg, being one of the few teams to win the race without having ever won a previous leg. (Amongst Eric&Danielle and Kisha&Jen)
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 huge deficits (for Max & Katie, not finding their car, getting pulled over and having to complete a speedbump; Joey & Meghan got horribly lost) and 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 the way to the Pit Stop and 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, 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 rarest moment you'll see this much team arriving on 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, but still being unable to make the flight. They made the flight and went from last to first 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 where the racer lands at the finish line.
Please give props to Eric (All-Stars) and Brendon & Rachel (20, All Stars 2). Finishing the race twice is a great feat by itself.
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 had never won a leg and were one of the not athletic teams in that season, they never used a Yield or Fast Forward, and in the final leg they surged from third to first while facing off against two quite strong teams.
In Season 1 of The Amazing Race Australia, Sam & Renae enter the penultimate leg at a huge disadvantage; not only are they the only females left on a race with brute strength rewarded over all, but they have also been "Marked for Elimination", which is nigh unbeatable without a Fast Forward as seen in every other version to use it. Not only that, but there were several equalisers on the leg as well, clumping every team together, robbing them of their previous time advantage. Any other team would have been pulverised - instead, they breeze through the final part of the leg at an unfathomable speed, they manage to check in first to the mat despite of another penalty they got for accidentally taking a private coach instead of a taxi, beat every other team on that leg in spite of that penalty, and become 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 had cops Shane and Andrew giving a child a little kangaroo toy after his grandfather helped him 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 them. Why? They ended up giving them out along the way to any kids 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 in only 2 tries even though most teams take more than an hour in such tasks, all despite having Parkinson's disease, and it was more complicated than average since 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 worst at the hockey task) and won over new fans with their positive attitude. 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.