Each anime has its own merits in its genre, so it's impossible to say which is the absolute best.
If I must list my favourite anime series,
1. Clannad ~After Story~ (very touching)
2. Air TV
3. Neon Genesis Evangelion (classic)
4. Wangan Midnight (> Initial D because there's an element of passion in it)
5. Naruto and Bleach (but they are too draggy, and my interest has diminished significantly compared to when I first started watching)
6. Sayonara Zetsubou Sensei series (satire)
7. Jigoku Shoujo series (ugliness of humanity)
8. NieA_7 (light-hearted comedy)
9. Welcome to NHK (comedic hikikomori life)
10. Hatsukoi Limited (good feeling)
11. Kurokami (unique story about doppelgangers)
12. Twin Spica (touching)
13. Gundam Seed (but dislike Destiny (2nd season))
14. Shakugan no Shana (1st season, 2nd season not so interesting)
15. School Rumble (lots of parodies)
16. Death Note (extremely unique)
17. FLCL (lots of musics!, and won't get bored even if you don't understand what happened... lol)
18. Lucky Star (very funny!)
19. Basilisk (historical setting and deep storyline)
20. GTO (funny guy)
21. NANA (very realistic)
22. Black Jack (touching)
23. Blood+ (interesting storyline)
24. xxxHolic (I love Ichihara Yuuko :3)
25. Yamato Nadeshiko Shichi Henge (very funny)
26. Eden of the East (unique story)
27. Honey and Clover (reminds me of something in the past)
28. Noein (unique story about alternate worlds)
29. Rurouni Kenshin (Kyoto Arc only... Shishio ftw)
30. Samurai Champloo (unique storytelling with hip hop (despite set during Edo period!) and I love the sword fights)
31. Trinity Blood (one of the first anime I collected)
32. Boys Be (probably my first anime collection if I recall correctly)
33. Ichigo Mashimaro (simply too cute!)
...and many more
See, told you there're TOO many to be named. These are the ones that I can recall at the moment.
Though I can tell you I hate just few anime in particular:
School Days
Suzuka
True Tears
Myself;Yourself
Ichigo 100%
Basically any anime in which there's always a guy surrounded with 5-6 girls who mysteriously love that guy for no apparent reason, and has only one guy friend who never had luck to have a girlfriend, acting only as a comic relief. Usually, the guy hurts everybody and have good ending for himself in the end getting the girl he wants. This is the usual pattern I see in love romance anime nowadays, which I dislike very much.
~Otaku...