When she, Bart and Lisa were shipped to a foster home (the Flanders) Maggie was the quickest to adapt and almost joined them until she noticed Marge.
Perhaps Maggie's most strained relationship was with her father, Homer but due to his incredible laziness he neglected Maggie and when they do try to bond, Maggie sees her father as a kind of monster and actually tries to run away, she also developed a father-daughter relationship with Moe the bartender but the two still love each other and Maggie has more than once saved Homer's life.
However, she keeps her intelligence a secret in order to be babied.
This is first revealed when Marge gives her a new pacifier, and when Marge isn't looking she smokes it like a cigarette.
Because she rarely ever talks, Maggie is the least seen and heard in the Simpson family.Even for a child her age, showed extremely violent mannerisms and a surprising amount of physical strength.Not to mention she said her first word, "Daddy" after Homer tucked her in and kissed her goodnight meaning it's clear that she loves him as much as he does her.Maggie's strongest relationship was with her mother, Marge after being transported to a foster family.
Maggie's almost joined the Flanders until she saw Marge once again "and became a Simpson again." At the beginning Maggie seemed to rely on Marge and the likewise but eventually she became fiercely independent as she was able to plan a Great Escape-style breakout from a daycare centre to get her pacifier back, she was able to save her father from drowning and rescue Homer from a mad tow truck driver.
Despite being a baby, Maggie is likely to be the most mature member of the Simpson family.