Gundam Seed and it's sequel, Gundam Seed Destiny. Except it's about not just the boy and his friends against the world, but futuristic space colonies as well so they can stop it and the world from killing each other.
Fullmetal Alchemist, or Fullmetal Alchemist Brotherhood. Not exactly against the world, but a boy, his brother, and his friends that eventually end up fighting against an all powerful government that controls a portion of the world.
Zone of the Enders: Dolores i. An anime that takes place in the same universe as the Zone of the Enders videogames and happens inbetween the first and second games. An old school dad, along with his estranged son and daughter, end up on the run from the Earth government while trying to find out the truth of what happened to the protagonist's wife, and find themselves up against a force on Mars as well. Oh, and besides his kids, he also has a giant sentinet robot traveling with him as well in tow.
Trigun. A crouching moron hidden badass travels from town to town on planet who's government placed a giagantic bounty on his head after he "supposedly" destroyed an entire town. He has misadventure after misadventure, being tagged along with by insurance girls and occasionally a badass priest, while searching for something.