MOTHER (1989, Famicom): The series' debut, telling the story of Ninten as he works to uncover his family's connections to an impending alien invasion. Wasn't released outside Japan, but a prototypical English version, widely called "EarthBound Zero", was discovered in the late 1990s.
Big Bad: Giygas and Porky for the whole series. In fact, these two are what connect each game to each other: Giygas's defeat in the first game drove him insane and turned him into the monster who we see in the second, and Porky's manipulations and time travel abuse both make him a recurring antagonist in the second game and the main villain of the third.
Book Ends: A quite brilliant one in fact. The major one you find is MOTHER 3's title logo, which starts off with a half-wooden and half-chrome design. When the game finally ends, the logo is back to all wooden, with a Earth instead of the chrome O. This is the logo to MOTHER 1.
Everything's Deader with Zombies: Zombie mooks pop up time to time. In MOTHER, you see them the early graveyard section of the game and Rosemary Manor. EarthBound's Threed has been completely overwhelmed by zombies, trapping them in a perpetual George Romero movie. In MOTHER 3, the cemetery north of Tazmily Village when you take control of Duster in Chapter 2 comes up with some as well.
From Nobody to Nightmare: Two examples, both roughly of the same age when they begin their descent: Giygas, originally an infant alien who expressed curiosity about his human co-passengers, to the literal embodiment of all evil; and Porky, a comic relief character who is chosen to be Giygas' representative on Earth. Porky turns out to be the most sadistic character in the series.
Genre Deconstruction: MOTHER is Itoi's meditation on what games are, why they are fun, and the logistics of applying JRPG logic to the real world. For example: Who designs dungeons? And why do people instinctively know to loot them? (Admittedly, the series' mythos got a little deeper with each game.)
Gotta Catch 'Em All: The Eight Melodies in MOTHER and EarthBound. In MOTHER 3, Lucas is in a race to stop all Seven Needles from being uprooted (or, when failure there becomes inevitable, make sure that he's the one that pulls them).
Hello, Insert Name Here: A prominent example, as this feature is used to name the game's most powerful attack and the food your mother gives you to eat every time you see her.
Not to mention the name of your dog, the friends that you will make along the path of your journey, and the um... "flavor" of the text boxes.
And you are able to give your own name as well as that of the main group. This can easily put the insanity of Giygas into perspective should you name yourself or Ness after him.
Our Time Travel Is Different: Ness' party travels to Giygas' lair, a cavern at the center of the Earth teeming with plant life, but it's otherwise empty. They deduce that Giygas is attacking from the distant past, and use Dr. Andonuts' phase distorter to send them there.
After disappearing at EarthBound's climax, Porky got lost in extensive time travel abuse, to the point where by the time of MOTHER 3, it's warped him to be an immortal old man with the mind of a child.
Police Brutality: In EarthBound, the cops attack Ness just because he refused to read the "DO NOT ENTER" sign at the traveller's shack leading to Giant Step, despite the fact that he clearly received the shack's keys from the equally incompetent Mayor Pain B.H. Pirkle.
Serial Escalation: One of the largest plot points in the second and third games? How many times can Porky Minch ruin everyone's lives. And boy, does it escalate.
Sheathe Your Sword: A full-on assault on Giygas/The Masked Man is pointless. To win, you have to eschew violence (the antithesis of every JRPG at the time) and instead appeal to the humanity inside them.
Yin-Yang Clash: Just as Ninten and Ness are all about the melody, the main antagonists of MOTHER accordingly have dissonant theme music. (Incidentally, this is the first hint that Porky is going to be trouble.) Giygas has no melody at all, only an incessant, high-pitched ring.