Because you like Nana Komatsu in Nana
After Rintarou Okabe develops the Phone Microwave, some of his fantasies start to seem uncomfortably real. 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!.
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.
Though bold and pure of heart, Utena Tenjou has a fairytale vision of the world that can make her oblivious to its darkness. See them in Revolutionary Girl Utena.
When you live your life in public, like Mima Kirigoe, it's hard to know who you really are. See them in Perfect Blue.
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.
Char is always thinking two or three steps ahead of the enemy. See them in Mobile Suit Gundam Series.
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.
Shana is a red-haired warrior with a black-and-white worldview. See them in Shakugan no Shana.
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.
Konata Izumi has a live-now, worry-later view of the world. See them in Lucky Star.
What Mako Mankanshoku lacks in common sense, she makes up for in sheer optimism and force of personality. See them in Kill la Kill.