PSP Shakugan no Shana 

Sakai Yuuji, a high school student who expected his normal life to last forever, is dead. When he was on his way home he witnessed a shocking view as the world suddenly froze: people were engulfed by blue flames and a monster resembling a large doll swallowed them. Just as the monster prepared to consume Yuuji, a sword-wielding girl in black attire with flaming red eyes and hair that burns like embers saved him from the monster. The girl called herself a "Flame Haze" who hunts the "Guze no Tomogara", creatures from another world. As Yuuji noticed a blue flame in his chest, she called him a "Torch", a temporary replacement, saying that the "real" Yuuji's existence had already ended. Unfazed, Yuuji befriended the strange girl, named her "Shana", and joined her fight against Tomogara and other Flame Hazes.

Blue Dragon AMV - V6

My first try on AMV, thanks to Churchie for the guide :)

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PSP Ergo Proxy

 PSP Serial Experiments Lain

 Genre: Cyberpunk, Drama, Mystery, Psychological, Science fiction

The first episode opens with the mysterious suicide of a high-school girl, chisa yomoda. chisa-chan was a classmate of lain iwakura, a quiet, 14-year-old high-school girl. one of the other girls in the class has been receiving e-mail messages from chisa-chan, and lain discovers she also has mail from chisa-chan. In the mail she explains lain that she just abandoned her flesh. she assures lain that she still is alive in the 'wired'. After getting a new 'navi' and adding a 'psyche' circuit, lain spends more and more time in the wired. It seems that Lain has at least 2 personalities, and lain's first personality is even changing.