1. Welcome to the NHK (anime) - great series, short and sweet. The anime version is better than the manga version, as they tell minor different storylines. Very human characters, funny, and sad. A tear-jerker.
2. Death Note - I'm a sucker for its dark atmosphere. Light and L rivalry is probably the best rivalry in any anime I've seen. Also, I love how the main character is a villain while the antagonist of the series is the hero.
3. Detective Conan - The first hundred episodes had absolutely great cases (Masked Villa Murder Case anyone?), however, the one thing that makes DC different from other plot-less mystery Law and Order/CSI shows is the Black organization development. Haibara Ai kept me following the series, add on the confrontation of her with the Organization, and the introduction of Vermouth, the CIA, and the FBI, the show can get extremely interesting. However, the series has been going for far too long and thus the fans are showing fatigue, which is why it's not my # 1 and 2.
4. Bleach - great art style. Kubo can draw. Unforunately, his story telling could use some work. The introduction of Rukia and Ichigo was great, along with Soul Society. Hueco Mundo wasn't bad either, it might have been repetitive, seeing how it was now Orihime kidnapped instead of Rukia, the Espadas were a great bunch of characters. However, the series took a nose-dive with the conclusion of Aizen and the Fullbring arc. Hopefully, the series will go back to being respectable. Bleach gets on my list for it's awesome characters and artistic vision.
5. Durarara! - I really enjoyed this colorful series of hectic fun. All the characters were unique, the artstyle was very nice, and the story had that supernatural twist to it that just intrigued me. More importantly, the characters- Celty, Izaya, etc. Here's hoping that it's going to get a second season