It's amazing how many people don't realize how connected Pokemon is to the Mother (Earthbound in North america) series. Since the tradition and formula from the first game is always carried over, we will probably always have some variation of Mother homages in each game.
. Earthbound also helps explains the inspiration behind Red and any other absent protagonists parent's, including Ash/Satoshi. It's so heavily speculated that he reason Red's father is absent is because Ness' father was absent too. He only calls you on your phone. Ness' father was was based on Itoi's own life. He was always busy and never had much time to spend with his kids. Because of this, the Pokemon games will always carry the tradition of having a father somewhat based on Itoi. That's pretty huge for Mother/Earthbound fans. Pokemon is much popular and will always have sequels.
Mewtwo is an homage to Giegue, specifically his appearance in Mother 1. Mewtwo and Giegue also share strong psychic powers, and Mew is speculated to have originated from space. According to dialogue from the games, Mewtwo was born from a pregnant Mew and became bitter about his relationship. This would make Mew his Mother. It's also a little bit similar to how Giegue became twisted, hateful and bitter about his origin. Also It's interesting to note that Giygas' appearance in Mother 2 is rumoured to have the appearance of a Fetus. Mew actually is based on an embryo. (I just like adding fuel to crazy theories, so ignore that last part if you don't like those weirdo giygas theories.)
It's speculated that most of the species of Pokemon have originated from space. (Link) More specifically, Clefairy, Deoxys, Lunatone and Solrock, Kyurem, are said to have arrived on a meteorite. In Mother 2, a meteorite falls from the sky. BuzzBuzz, a talking Dung Beetle emergeces and helps Ness fight off the invading aliens with psychic powers.
The style of the overworld maps for both games are very similar. Red may be based on Ninten or Ness' appearances due to the iconic red hats and backpack. Both character's are rivals with their neighbors. For Ness it's Porkey and for Red it's Gary. The movie 'Stand by Me' was one of Shigesato Itoi's inspirations for the Mother series. Link. ) It can be seen on TV in the first generation Red/Green/Blue and Yellow games. There is an item in Mother 2 called the Rock Candy, which permanently boosts your stats. It's similar to the Rare Candy from the Pokemon Games which levels up your pokemon.
It's been confirmed many times that some people who worked at Ape went on to work at Gamefreak. This is probably the reason why Lucas and Pokemon Trainer were paired up in Brawl.
The Mother/Earthbound series is so underappriciated. I think it's so ironic that Pokemon has a massive following, and most people have not even played the game that inspired it. It's a brilliant game on it's own right, Mother 3 comes close to literature at times. It's heart breaking. Some of the most discussed about things in the Pokemon Universe are directly inspired from it, and copied every game! The reason why Red/Ash doesn't have a father, the origins of Mewtwo and all Pokemon according to really popular theories. Mother fans may only have 3 games, only one of which was officially released, but the style lived on through the massively popular Pokemon games.