I had a list like this before, but I've recently got a ton of new anime on my list so therefore more stuff to post.
Here's a compilation of all my favorite anime openings and endings. 1 through 5 are in order for each list, the rest not really at all. These are based off of both visuals and song.
1. Cardcaptor Sakura OP 3 - Platinum
2. Attack on Titan OP 1 - Guren no Yumiya
3. Sword Art Online OP 2 - Innocence
4. Sailor Moon OP 2 - Moonlight Densetsu
5. Amensia OP 1 - Zoetrope
6. Clannad After Story OP 1 - Toki wo Kizama Uta
7. Guilty Crown OP 1 - My Dearest
8. ef - a tale of memories OP 1 - Euphoric Field
9. Fullmetal Alchemist: Brotherhood OP 1 - Again
10. Durarara!! OP 2 - Complication
11. ef - a tale of melodies OP 1 - Ebullient Future
12. Code Geass R2 OP 2 - World's End
13. Mawaru Penguindrum OP 1 - Nornir
14. Air OP 1 - Tori no Uta
15. Kanon (2006) OP 1 - Last Regrets
16. Hidamari Sketch x Hoshimittsu OP 1 - Dekirukanatte☆☆☆
17. Yuru Yuri♪♪ OP 1 - Yes! Yuyuyu☆Yuru Yuri♪♪
18. Neon Genesis Evangelion OP 1 - Cruel Angel's Thesis
19. Guilty Crown OP 2 - The Everlasting Guilty Crown
20. Sword Art Online OP 1 - Crossing Field