Winry lives in the quiet countryside of Resembool, where she was raised by her grandmother from her dad's side. Her parents were brilliant doctors who helped out in the Ishvalan civil war, and they were killed by their own Ishvalan patient--Scar (who, at that time, was unconscious).
Winry is not only there because she is Ed's mechanic, but she is the constant support of both Ed and Al, and she represents the "normal" person of the FMA society.
Not only did she give Edward an arm and a leg, but she also helped a mother deliver a baby, saving both of their lives. She helped Al make up with Edward after they had a quarrel. Winry also helped rid Scar's (who had killed her parents) vengeance against State Alchemists--she actually tends to his wounds, and she cleverly uses herself as a "hostage" of Scar to distract the enemy.
In the end, she is an important part to the plot in FMA, and without her, some things would have been left out or changed completely.
Winry accepts Edward's proposal two years later after the defeat of the antagonist in FMA (Father), and they get married and have two children (an older boy and a younger girl) in the future.
FMA fan 2: "That one mechanic that's always paired up with Ed? She's sooo useless! She never does anything important, and she's only there to be Ed's mechanic. And Ed's MINE!"
FMA fan 1: "Uh, go read the manga...because obviously, you're still a newbie to FMA."