Just about anything Proto Man related, specifically when he deletes Magic Man, Quick Man, and Bubble Man each with one stab from his sword. Albeit Mega Man's the one who weakened them, but still.
DesertMan's scenario. When Sunayama's finished explaining his Evil Plan to Chaud, just as Chaud is about to hand his PET over to the villains... Lan spins around a corner, shouts "MEGAMAN, ATTACK!", and tosses his PET case, MegaMan and all, right at Sunayama's head (as you can imagine, this doubles as a Crowning Moment of Funny). In a series where almost all combat is virtual, this was very refreshing.
In the fourth game, ShadeMan, who's completely immune to MegaMan's attacks, demands that he and Lan return the DarkChip they found. Out of options, MegaMan tosses him the chip... and then shoots it in midair, destroying it. ShadeMan is not pleased. (Fortunately, MegaMan gets a way to damage him in the ensuing battle.)
In the sixth game, MegaMan gets taken over by a giant Internet monster Sealed Evil in a Can, and you have to drag someone else' Navi (Heatman or Aquaman, depending on version) into Internet Hell to defeat him. As much as that could be a Moment, given that you just defeated the main character fused with a massive cybermonster while playing as either a baby with a fishbowl on his head or a manic zippo lighter, that's not the awesome. A few scenes later, MegaMan wakes up from his beating... and the Beast roars back to life. Lan and his dad are panicking. And then your substitute Navi Bright Slaps Rock back into control. Win.
Actually, by that time (when you need to save him from that cult in the Undernet, not when MegaMan first absorbs Gregar/Falzar), I believe you already have the first three crosses(Aqua/Heat + Tengu/Slash + Tomahawk/Elec), so you can use any of those three. Saving MegaMan with Elecman has never felt so epic.
And following the last prelim of the contest, you have access to all Link Navis. So, technically, you can send the Grim Reaper into the underworld to go save MegaMan.
Again in the fourth game, this troper considers the ending a crowning moment of awesome. After defeating Duo.EXE, and with only an hour before a computer-controlled asteroid collides with the Earth, MegaMan tries to move the wheel controlling it, but it would not even budge. However, after the whole world starts to cheer for him, Lan goes Full Synchro with MegaMan, and the wheel that wouldn't even budge now spins so hard that it's a surprise that it doesn't fly off its axis. With the music to go along with it, it was perfect.
Let's be honest, Mega Man does something selflessly heroic and suicidally stupid at the drop of a hat to the point where it stops being awesome sometime around game 2. That said, the ending of BN3 felt like they finally figured out how to do a proper Heroic Sacrifice with all the awesome due to such a moment. Even his resurrection after the credits is so well done as a CMOH that finally, FINALLY Mega has some Awesome in his pants. And then they hit us with BN4...
Anyone forget Wily's CMOA at the end of MMBN5? He's an old man who walked into an EXPLODING VOLCANO, just to use a brilliant combination of the Reset Button and a Bright Slap to allow his own son a chance at redemption, and BOTH of them survived!
From MMBN5: Team Colonel, Baryl Bright Slaps Lan/Netto out of a Heroic BSOD and tells him to quit whining and kick ass. He does that, and you get to control COLONEL HIMSELF!
Team Protoman gave us Protoman's exclusive unbridled awesome, and Enzan/Chaud took a punch from Lan and turned it into a Rousing Speech that basically said "take that aggression, and do something positive with it".
MMBN3: The entire scenario where Lan and Mega Man are kicking viral ass to save Mamoru from dying was so Manly Tears inspiring that the whole scenario is a gigantic CMOA for the series in general!
MMBN4: For those who say this game sucked, here's one moment of awesome no one can deny. Lan made some very questionable moral decisions throughtout the game, and Regal's attempts at a What the Hell, Hero? speech at the end were destroyed by the simple fact Lan still gave a damn about humanity, and Regal didn't. The game's story was thin, but it was a barely disguised morality tale that proved that those who ultimately see the good in humanity and are willing to fight for it are the best hope our race has of survival....literally.
Bonus points for being the impetus that gave Lan, Yuichirou, AND Wily the chance to ultimately prove that point by the end of MMBN5.
MMBN6: Joe Mach's awesome Spanner in the Works, courtesy of beating the piss out of his former World 3 allies because his conscience couldn't stand the thought of those assholes hurting a child.
Back to BN5, there's the Brain Navi of both games beating the living shit out of the impostors of himself and MegaMan. Cool when SearchMan does it in ProtoMan, but more awesome in Colonel, considering the fact that your Brain here is NumberMan.
The very end of the series. MegaMan has been taken over by the Cybeast. Lan can't do anything to save him. The Megabeast then warps over to Iris and Colonel, weak from fighting the opposite Cybeast. The two unite to form the original Colonel with the emotion that became Iris. Colonel then rushes at the Megabeast, tears the Cybeast soul out of his body in a single strike and then performs a Heroic Sacrifice to destroy it once and for all.
The games themselves usually highlight moments of awesome by setting them to a rendition of each game's main theme. Special credit, however, goes to the Gamecube spinoff Network Transmission: this game doesn't use its own main theme for heroic moments, they use Kaze wo Tsukinuketenote Break Through the Wind. It's awesome charging towards the Final Boss with the triumphant refrain of the anime theme carrying you forward.
Also, from Network Transmission, if you avert doing Not Quite The Right Thing, you get to take the Professor out with style. While the Professor taunts Lan and Mega about how defeating the Life Virus R didn't ultimately stop him, his mockery dies in his throat when he realizes the Officials are on his doorstep. Turns out, Zero owed them a favor for sealing the virus he was generating, and used the leftover viruses infecting the Professor's own computer to sniff him out.
The fight against Serenade.EXE is also awesome. That MegaMan gets crowned King of the Undernet for winning is the cherry on top.
The Bonus game content for both the third and fifth games are each minor story arcs unto themselves, each culminating with a Final Battle against a Bonus Boss with some of the heaviest Super Weight in the entire plot. As tough as it is to get there, the payoff is entirely worth it.
After rescuing one of your opponent's navi from being offed by the mafia, their boss overhears their plan to off her. When they go to attack her, the screen goes dark for half a second and you see both the attackers on the ground. Not bad for an old lady.