The Mega Man series (sometimes called "Original" or "Classic"), which started the franchise, starring Rock, the creation of Dr. Light, fighting against the forces of Dr. Wily in the year 200X — 20XX from the third installment on. (1987);
Mega Man Legends (Rockman DASH in Japan), set at least 4,400 years after the ZX series with a new, seemingly-human Mega Man, bearing the ridiculous sounding name "Mega Man Volnutt." (1998)
Mega Man Battle Network (aka Rockman.EXE) series, which occupies an Alternate Continuity of 200X where Dr. Light (here known as Dr. Hikari, Japanese for "light")'s network research won out over Dr. Wily's robot research; (2001)
Mega Man Zero, set 100 years after the "Elf Wars" which appears to be 100 years after the end of the X series. This stars the Ensemble Darkhorse Zero, now a freedom fighter trying to free the last remaining Reploids against a tyrannic government; (2002)
Mega Man ZX, set 200 years after the Zero series, where mankind has been fully merged with Reploids. The problem of Mavericks is still a threat, although the cause for the outbreaks is entirely different. Otherwise normal Humanoids use Biometals to take the form and powers of heroes of old; (2006)
Mega Man Star Force (in Japanese, Ryuusei no Rockman or Shooting Star Rockman), a series that takes place 200 years after the Battle Network games, where Cyberspace and the human world are even more intertwined via Wi-Fi radio; (2007)
Rockman Xover (pronounced "Crossover"), a Crisis Crossover RPG game for mobile devices, designed to celebrate Mega Man's 25th anniversary; (2012)
Rockman Online (Korea only, for now at least), set at an unspecified point in the future. After an era of peace, enemy robots based on Classic series Robot Masters and X series Mavericks suddenly attack. The government of this time period, the United Continent Association, responds by reproducing the heroes of these series (X, Zero, and Duo for starters) to combat the threat, which originated from a separatist organization called the Ultimate Reploid Association. The team behind it disbanded, and it was confirmed to be cancelled.
Alternate Company Equivalent: The Krion Conquest for the NES, made by Vic Tokai, goes so far in copying Mega Man as to use the same run cycle, similar power meter and highly similar death animation for heroine Francesca; copy several of the enemy and level appearances; and give her equivalent powers such as a Charged Attack and a Rush/Item-2 replacement in her broomstick. However, unlike Mega Man, she can duck and fire upwards. Still, it flirted dangerously close with Plagiarism.
Capcom DID use the "Alert" sequence from that game during later Mega Man games when you are entering a boss battle (see Krion Conquest's trope page). You know that "Warning" sequence that takes place that started with Mega Man X4 on (and even appeared in Mega Man Powered Up, the first time it appeared in a "classic" Mega Man game)? Krion Conquest actually did that first.
Artifact Mook: The infamous Metools. In the original Mega Man game the little hard hat guys appeared only on Guts Man's stage, which had the look of a quarry/construction site. (Guts Man himself appears to wear a hard hat) however they have since appeared in every Mega Man game on multiple levels and in massive numbers to the point that they are the most common enemy encountered.
Astral Finale: Most of the Game Boy series have their final levels take place in space (the fifth game does not count due to half the boss roster residing in space levels, and the only game to completely avert the space setting is the third one). As for the main games, Mega Man 10 saves its very last stage for this trope, right after the usual four stages of a traditional endgame castle.
Nintendo Hard: The whole franchise has a reputation for putting out very difficult games. The classic and Zero series especially stand out.
Not Me This Time: Meta-example. After Mega Man Universe and Legends 3 were cancelled, the iOS port of Mega Man X, and Rockman XOver, when Rockman Online was cancelled, fans jumped to the conclusion that Capcom was continuing their anti-Blue Bomber antics. It turns out that the troubles likely were on the part of NeoWiz, behind Rockman Online. (The game had been in Development Hell really since it was announced). Not that the fans care about it...
One Bullet at a Time: The side-scrolling games typically limit you to three uncharged bullets onscreen at a time. Later games sometimes include ways around this, and extra characters typically have different limits.
Orange/Blue Contrast: Considering the main character is very blue, this is pretty much a given. More obvious in the series' artwork than the games themselves.
Out of Focus: With Keiji Inafune having left Capcom, the entire Mega Man franchise has become borderline non-existent. Street Fighter and Resident Evil have been pushed as the new "crown jewels" of the company, with Ryu supplanting Mega Man as the new Capcom Mascot.
Power Crystal: On several robots and later Reploids, got especially common after X.
Power Copying: Mega Man has the ability to copy a major enemy's power, usually when it gets destroyed.
Robot Hair: Most reploids from the series (although the eponymous character hides his under his helmet most of the time). Mega Man ZX justifies the trope by explicitly saying it was an attempt to "making humans and reploids closer to each other to make better peace":
Most famously, Zero's long blonde ponytail from Megaman X.
Roll sports golden locks neatly tied up with a ribbon, whereas Plum (from Rockman Battle & Chase) has pink hair.
Mega Man Zero has Elpizo (blond), Omega (a pinkish/fuchsia ponytail sprouting out from the top of his helmet), and Kraft (dark spiky hair which appears to also form Go Nagai Sideburns), among others. Seeing as Omega's body is a shell/Power Limiter for Zero's original body, this means that Omega also shares Zero's infamous Rapunzel Hair.
Splash Woman (from Mega Man 9) and Fairy Leviathan fall into the "Mechanical Facsimile" category: their helmets frame their faces in a manner that resembles hair (specifically, a Sci-Fi Bob Haircut, with a few extra bangs in front in Leviathan's case).
Self-Imposed Challenge: Several, but a common one is to beat all the bosses (Including in the final levels) using only the arm cannon. Or without taking any damage.
This becomes the basis for several in-game acheivements in 9 and 10.
Single Use Shield: the Spike-Barrier/Shock-Step/whatever-it's-called, which protects you once from the instant-death spikes. But you have to jump to safety before the Mercy Invincibility wears off, or....
Video Game Long Runners: as of 2009, the series ran for over 22 years, and there are 7 series, each of which have numerous installments on their own. The description section at the top of the page tells it all.
In the X series, it is discovered that The Virus that turns Reploids into Mavericks originated from Zero, and both were Wily's final creations before he died long before the X series. The Big Bad of the X series, Sigma, merges with the Maverick Virus and transforms it into the Sigma Virus.
In the Zero series that comes after the X series, Dr. Weil (no connection to Dr. Wily according to Word of God) creates Omega as a Dark Messiah to exterminate all Reploids. Omega's consciousness inhabits Zero's original body since Zero's mind was extracted after the X series. The Mother Elf, who becomes the Dark Elf, another major antagonist, was created by Ciel's ancestor by studying the Maverick Virus and trying to create an antibody.
In the ZX series, all the Biometals are created from studying the original Biometal Model W, created from the ruins of the Ragnarok satellite that Weil fused with at the end of Zero 4.