Here are my choices for Lanterns from across the multiverse.

Rage:

Azula from Avatar the last airbender. Zukos sister and a firebending prodigy she also had a deeply held rage for having to be perfect in her fathers eyes and her mother preferring Zuko over her, which led to an emotional breakdown at the end of the series. She is cold calculating rage incarnate.

Natsu Dragneel: A powerful dragon slayer mage from the fairy tail guild Natsu is an impulsive person rule be his emotions particularly passion. Though he can erupt with the rage of a dragon his altruistic gregarious nature helps balance out the rage of the red ring.

Greed/Desire:

Treize Khushrenada from Gundam Wing. a brillinat military leader, Treize was not rule by desire, but mastered it and used it to achieve a peaceful world. He has the strength of will to master the power of desire for his own ends.

Ichigo Kurosaki: A young man with orange hair and a soul reaper, he is driven by the overwhelming desire to protect those around him. The power of the Orange ring can cause him to be overbearing, but he is able to control himself (most days)

Fear:

Terra from the teen titans animated series. The fallen titan, but still a hero unlike her twisted comic counterpart, Terra inspired fear first through the lack of control of her powers and then under Slades tutelage when she terrorized jump city. Can she still be a hero utilizing the yellow light of fear?

Casshern: A robotic Cyborg from a post apocalyptic world, Casshern was the cause of a great catyclysm that left his world a ruin, inspiring fear in the populace for his actions.

Will:

Shinji Ikari. Even though he was literally rendered down to goo during third impact, he chose to come back to humanity and live with the possibility of being hurt. Say what you want but through all his whining he had the will to keep trudging through hell all the way to the end and back. I believe he has what it takes to be a green lantern.

Naruto Uzumaki: An orphan after a monster attacked his village, Naruto grew up hated and feared due to having that monster sealed inside him. He never gives up and pursues his goals to the very end, the epitome of a green lantern.

Hope:

Relena Peacecraft: The female lead of Gundam Wing, Relena is the angel of the battlefield that helped bring peace to the war torn world, and inspired hope every step of the way.

Sonic the Hegehog (Archie Comics version). The hero of mobius and greatest of the freedom fighters, Sonic inspires hope in the populace in his never ending fight for freedom and do it to it attitude.

Compassion:

Avatar Aang: The main character of Avatar the Last Airbender Aang is a pacifistic and Compassionate air bender. He can manipulate the four elements and it has been revealed that the indigo tribe can manipulate the other emotional lights.

Liono (2011 version) The young lord of the thunder cats, Liono forgoes the cultural arrogance of his people for compassion and empathy for those around him no matter what species.

Love:

Will Vandom: the leader of W.I.T.C.H. a team of young girls who can wield the power of the elements, Will wields the power of Quintessence absolute energy. She is also a naturally loving and caring person, especially to her boyfriend Matt.

Utena Tenjou: A beautiful girl with a tomboy streak, she is graceful and elegant while still being strong with excellent swordsmanship skills. While naturally compassionate her deep love for anyone she considers a friend makes her a star sapphire.