Because you like Kallen Stadtfeld in Code Geass
For the sake of science, Kurisu Makise will persevere no matter how deep into the dark secrets of the world she finds herself. See them in Steins;Gate.
Yuri is living in the afterlife, which takes the form of a high school where no one dies. But if you follow the school's rules and live a "normal" life you vanish. See them in Angel Beats!.
Kagami Hiiragi keeps her grades up, helps at Takanomiya Shrine, serves as class president, and hangs out with her friends. See them in Lucky Star.
An alien, a time-traveler, and an esper are following Haruhi Suzumiya, who – unknown to herself – is a near-omnipotent reality warper. See them in The Melancholy of Haruhi Suzumiya.
From secret organizations to alien attacks, Kyon's life has been one weird, unexplainable thing happening after another. See them in The Melancholy of Haruhi Suzumiya.
After Rintarou Okabe develops the Phone Microwave, some of his fantasies start to seem uncomfortably real. See them in Steins;Gate.
China has five thousand years of history, and he's optimistic he'll win over the Allied Powers to the wisdom of his ways. See them in Axis Powers Hetalia.
With most of the people that Sango loved now gone, the only thing she wants is to kill the demon who destroyed her village. See them in Inuyasha.
After alien Haruko rides in on her Vespa, giant robots spouting from Naota Nandaba's forehead soon become the least of his worries. See them in FLCL.
There are rumors that the Spirit was an Egyptian Pharaoh in his past, but without any memories, he doesn't know how true they are. See them in Yu-Gi-Oh! .
As the Rose Bride, Anthy Himemiya is a spectator in the fencing matches fought over her and her power "to revolutionize the world." See them in Revolutionary Girl Utena.
Fate has forced Amuro into the terrors of war, and he must use the Gundam and all of its power if he is to make it out alive. See them in Mobile Suit Gundam Series.