According to poll conducted at Biglobe site, mahou shoujo anime Puella Magi Madoka Magica topped rankings on most depressing anime series with 186 out of 1,664 who voted.

Also in the list are SchoolDays, Jigoku Shoujo and Dog of Flanders in which said anime series shows death of one or more of its characters.

Rankings

1. Puella Magi Madoka Magica
2. SchoolDays
3. Grave of the Fireflies
4. Bokurano: Ours
5. Neon Genesis Evangelion
6. Higurashi no Naku Koro ni
7. BLOOD-C
8. Hell Girl
9. Elfen Lied
10. Inu x Boku SS / Ano Hi Mita Hana
11. 5 Centimeters Per Second
12. Mawaru Penguindrum
13. Yosuga no Sora
14. Umineko no Naku Koro ni
15. Kamisama Dolls
16. Saikano
17. A Dog of Flanders
18. Kimi ga Nozomu Eien
19. Fafner in the Azure
20. Tokyo Magnitude 8.0
21. Black Lagoon
22. Mobile Suit Victory Gundam
23. Full Metal Alchemist
24. Narutaru
25. Shuffle!

[Source]