Althought I've seen all animes on my blog and some others that are best remaining unknown, it doesn't really make this list precise, also this is based on my opinion on good/best animes.
1- Death Note
Death Note besides being my first anime ever, the one that enable me to enter in the anime world, but is also a genius anime, the ones I enjoy the most. The best part of the anime is really the fight between Light and L focusing on the tennis match :P.
Well Naruto will always be one of best animes, due to the HUGE story behind it, maybe one day even surpass Death Note for me, but as we can only watch one episode per week, it's sad.
Bleach, as Naruto, the anxiety of waiting for next episode drives me crazy but I also consider one of the best. First episode is just so LOL, when Rukia enters in Ichigo's room, and Rukia's drawings
4- D. Gray Man
D. Gray Man, great anime very good story, akuma, exorcists, innocence, everything is so interesting. Hope the episodes after 103 come soon, I'm waiting for them.
5- Full Metal Alchemist
Full Metal Alchemist, the alchemy and how they use it really is awesome.
6- Darker than Black
Darker Than Black with contractor, each with it's unique power. When I saw the first episode of second season, gimini of the meteor, is perfect as always.
7- Prince of Tennis
Prince of Tennis is an anime about tennis, very addictive, not because is tennis nor sports, I absolutely hate any type of sports and loved this anime.
Trying to change the animes we always see on lists we have Rideback, (look at the link and see the info, its a must :P) don't be scared with the image, I must say even I got scared when I saw this part in the first episode, but turns out to be an explendid anime. You need to check it out.
9- Skip Beat
Skip Beat, Kyoko trying to revenge finds what she really likes doing, and turns like in the picture :p, also waiting for SEASON 2 but I guess it'll take time :(.
10- Eureka Seven
Eureka seven is the first airship like anime I've ever enjoyed. I normally avoid airships and airspace animes.