I don't own the rights to any of these animes/songs, and all credit goes to producers and artists. This is not the definitive list of 10 best anime openings, just some stuff that I like. Feel free to comment on whatever or add some suggestions.
Recap: 10. Steins;gate. Song: "Hacking to the gate, by Itou Kanako" 9. Trigun. Song: "H.T. by Tsuneo Imahori" 8. Samurai Champloo. Song: "Battlecry, by Nujabes feat. SHING02" 7. Black Lagoon. Song: "Red Fraction, by MELL" 6. Tengen Toppa Gurren Lagann. Song: "Sorairo Days, by Shoko Nakagawa"