Here are answers, sorry are a bit rough, I had rewrite them all hastily:

Spoiler ->1. Papa no Iu Koto o Kikinasai!
2. Another
3. Haiyore! Nyaruko-san
4. Tasogare Otome × Amensia
5. Binbougami ga
6. Jinrui wa Suitaishimashita
7. Sword Art Online
8. Sakamichi no Apollon
9. Ixion Saga DT
10. Sakurasou no Pet na Kanojo
11. The Big O
12. Amagami SS
13. B Gata H Kei
14. Kodomo no Omocha
15. Tonari no Kaibutsu-kun
16. Majokko Tsukune-chan
17. Busou Shinki
18. Polar Bear Cafe
19. Gintama
20. Space Brothers
21. Hayate no Gotoku! - (Lucky Star)
22. Zettai Karen Children - (Hayate no Gotoku)
23. Natsu no Arashi - (School Rumble)
24. Mayo Chiki - (Hidan no Aria)
25. Asobi ni Ikuyo - (Kampfer)
26. Equal Romance by Prière - Cover of 2nd Ranma 1/2 ED
27. Zangoku na Tenshi no Teze by Hinagiku Katsura (c.v. Shizuka Itou) - Cover of Neon Genesis Evangelion OP
28. Hanamaru Sensation by Hatsune Miku - Cover of 1st Kodomo no Jikan ED
29. Renai Circulation by Iori Minase (c.v. Rie Kugimiya) - Cover of 4th Bakemonogatari OP
30. Asterisk by SCANDAL - Cover of 1st Bleach OP
31. Clannad After Story - 7-5-3 celebration
32. Haruhi-chan - Setsubun
33. Umineko no Naku Koro ni - Halloween
34. Poyopoyo Kansatsu Nikki - Obon
35. Kimi ni Todoke - Hatsumode/New Year
36. Midori no Hibi
37. Mahou Shoujo Lyrical Nanoha
38. Ninin ga Shinbouden
39. Uta-Kata
40. Maria-sama ga Miteru
41. Yakitate Japan!
42. Kono Minikuku mo Utsukushii Sekai
43. Girls Bravo
44. Tsukuyomi
45. Paranoia Agent
Oh, and the mystery link; they were all TV series that debuted in 2004.
46. GJ-bu (Good Job-bu)
47. [email protected]
48. Senran Kagura
49. Fate/kaleid liner Prisma Illya
50. Hentai Ouji to Warawanai Neko