Haijime Saito vs. Rurouni Kenshin in Samurai X/Rurouni Kenshin
In Dragonball Z, Vegeta vs Goku in the Saiyan Saga. It was so much better until they thought of the Super Saiyan ability.
Suigintou vs. Shinku, in Rozen Maiden season 2.
Not really a battle though, but Nana vs the kids in Elfen Lied.

For the rest, I don't really watch animé like Naruto, Bleach and such. I watch Bleach, though. But I'm more into girly animés/mangas. Like, He Is My Master, Love Hina, Mahou Sensei Negima, Sailor Moon, etc.

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On the way, on the way home
i saw a rainbow beneath my feet
flowing over the filthy street
oh yeah