
* MOBILE SUIT GUNDAM (aka MSG, 1979, 1981-2) -- although the production values are relatively primitive by modern standards, the creation of the series is still one good place to begin, since easily 80% of the story concepts were invented here.
In the early 21st century, global human population problems lead to both the union of most nations under one federation, and also a project (spearheaded by the scientist and social visionary Daisuke Zeon) to migrate humanity into space colonies, orbiting the sun along the same path as Earth (with a few colonies also built on the Moon). By the mid-century, the first colonies are finished and in honor of this the calendar restarts at year 0001 of the Universal Century. (Gundam continuities are typically named after this new timeline restart, when humanity first starts permanently living in space, so this is the UC story, the longest set of stories in the series.)
By 0078, billions of people are living in dozens of massive satellites (each around 100 kilometers long) grouped in clusters (known as "Sides") at various points within sublunar orbit and along Earth's orbital path (preceding and following our planet around the sun). But the years of general peace as humanity fought the harsh conditions of space have dwindled to an end, for now that things are relatively comfortable and even idyllic in the colonies, agitation grows.
The revered doctor Zeon theorized that humanity would begin to evolve more quickly in its new habitat, leading to a new type of humanity (Newtypes) with greater intuition and mental powers, thus also leading to greater understanding among people, putting a final end to human war. But in his old age Zeon grew disillusioned with how the Federation insisted on meddling in colony affairs, and now that he has died (under mysterious circumstances) the Zabi family carries on a policy of colonial self-government based on the genetic and technical superiority of colonists over people still living on Earth.
With shades of both the American Revolution against Great Britain, and the transition of Imperial Germany to Nazi Germany, many colonies join the Principality of Zeon and rebel against the Federation government, while other colonies and clusters insist on neutrality. So in late 0078 a war begins (the "One Year War" in Gundam parlance). The Earth Federation has vastly more resources and manpower, but the Zeon Principality has much higher quality of troops and technology, including the first combat deployment of mobile suits (previously used for helping construct and maintain the colonies) as anti-ship weapons, too small and fast to target. (The mobile suits themselves, while visually personable, are not persons, just big flying tanks.)
Despite the superior quality of Zeon's forces, the Zabi family realizes the Federation will win any protracted war, and so take the drastic step of invading and gassing Federation (and some neutral) colonies, then reprogramming their orbits to crash onto the leading cities of Earth (known in Gundam lore as a "colony drop"). This kills 50% of humanity outright, and Zeon follows up with a ground invasion, hoping to put the Federation permanently out of commission.
(In later installments this "Operation British" seems to be retconned into being one neutral colony which was intended to be dropped onto the reinforced Federation military headquarters at Jaburo, on the Amazon River, and then due to problems en route was accidentally dropped on Sydney, Australia instead.)
The MSG series starts with all this having already happened, and follows a high-school boy, Amuro Ray, who lives in a neutral colony, where unknown to him his father is working on a prototype mobile suit for the Federation (which so far has fielded crappy units) made of an exotic lunar-titanium alloy known as Gundariam. Zeon forces, learning of this research, invade the colony to secure the new suit, and through a series of events Amaro ends up in the cockpit of the "Gundam" prototype suit, barely defending himself from Zeon attack and accidentally killing his father along the way without even realizing it (one of the first signs, after the "colony drop", that this series intends to play rough!) Amaro and several of his schoolmates escape his doomed colony with the help of the crew of a small but potent warship, the White Base (known to the Zeons as the Trojan Horse), where he becomes progressively embroiled in the war against the Zeon.
Along the way he meets a mysterious blond masked man working for the Zeon, Char Aznable, secretly one of the surviving children of Duke Zeon, seeking to retake control of the Principality from the Zabi family. Char and Amaro become frequent rivals on different sides of the war, and while the Zeon are typically presented as the villains there are broad moral shades on both sides. The White Base descends to Earth and tours across it for a while as Amaro learns to pilot his Gundam more effectively, eventually helping drive the Zeon off the planet for good and then returning to space for the final campaigns to stop Zeon aggression and bring justice to the Zabi family. With help from the captain of the White Base, Noa Bright, Amaro slowly matures from a selfish and depressed boy to a reluctant but competent warrior, saddened over being repeatedly forced to kill people in order to survive, but determined to bring an end to the deaths of the war.
MSG wasn't a big hit originally in Japan, combining a somewhat dour tone with much plot fluffing and filler. Essentially inventing the "real robot" anime genre in a market of popular super-robot shows, didn't help it either. It plays much better today as a fairly sophisticated literary work, but its producers (reasonably) kept trying to force the main author and creator of the series, Yoshiyuki Tomino, to lighten the tone and include more colorful characters and robot enemies for Amaro to fight each episode -- in other words, make it more like a super-robot show! Eventually the producers announced they would pull the plug at 43 eps (out of a planned 52, or two standard American seasons -- and the immediate producers had to fight to get more than 39 eps!), but that didn't phase Tomino as it meant he could finish out the series cleanly with less filler, though the rush in production aggravated his chronic depression.
(To be fair, the American anime network Toonami tried to air dubbed versions of this original series twice in the early 2000s, and canceled the screenings early each time. The production values of the series just don't hold up very well.)
One result is that when Bandai had Sunrise re-edit the series into a trilogy of 2-1/2 hour movies in 1981 and 82, to capitalize on the popularity of the return of Star Wars films to the theater, the 14 hour 20 minute series ran well trimmed by about half. So riding the coat-tails of
The Empire Strikes Back the movies earned enough profit to spark new interest in the series and inspired Bandai to commission Sunrise (and Tomino) to try again with a sequel series in 1985. The sequel, Zeta Gundam, was such a hit that the series has been in more-or-less continual production ever since.
Sunrise recently re-released MSG in its full North American series export as two DVD collections; but the three theatrical features (typically collected together) are in most fans' opinion (mine included) the better way to experience the first story, despite some plot jumpiness (as storylines are compressed and leapt between) and a lack of English vocal dubbing. The English subtitles are at least professional, and the animation while primitive by modern standards is cleaner than in the original series. The age of the series, even as the theatrical movie trilogy, admittedly makes it a bit hard for modern audiences to accept for its production values, so this isn't necessarily the
best place for any Gundam seeker to start; but its introduction of the archetypal Gundam story-formula keeps it important to the whole series, and certainly anyone wanting to track the progressive development of the series over the years will want to start here.
(By "here" I mean the compilation movie trilogy, not the series per se.)Toonami's trailer for its (attempt at) running the original series back in 2001. Optimus Prime approves its existence. :mrgreen: (The war doesn't rage "to the stars" however; more like from the Earth to the Moon. Amaro's "powers" aren't all that beyond imagination either.

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Update: since the time several years ago when I wrote this, Sunrise/Bandai have released a total remake series with updated animation (naturally) and a somewhat expanded plot. This expanded plot, largely dealing with Char Aznable (as might be expected), has come with some criticism from fans (as might be expected.

) I haven't seen it yet myself, so cannot comment on it -- but IN THEORY it would also be a good place to start.