I haven't watched many anime so I only have a short list.
5. Ginga Nagaberoshi Gin, Silver Fang
I have watched this show since I was a kid and enjoy it. The manga is also good. Probably the best story about loyalty I have ever seen. Nice music and themes, but the age shows through stock footage and coloring mistakes.
4. Tanoshii Moomin Ikka, Moomin
I was surprised to hear this IS an anime. My childhood was all about Moomins. Art style is glorious, music is amazing and you can watch the episodes in pretty much any order you want. It is a lot kid friendly than the original source material, and it teaches children important lessons about friendship and living with harmony with the world.
3. Digimon Adventure
The only Digimon Season I have ever watched to the end. Interrupted my Pokemon mania season and turned me into another kind of maniac. You think I was obsessed with FMA? This addiction leaves that far behind! The story is interesting, characters are good and fleshed out although not as complex as one could hope. Also, the ending was so sad, saying goodbye to your best friends.
2. Sailor Moon
Oh my, am I in for a treat. I love this show to bits although it can be very, very stupid at times. It is a balance between goofiness and mature. The show is incredibly beautiful, I have yet to see something to match that level. Despite the vast amount of pointless filler episodes, and one season that in the long run of things was totally unnecessary, this show is always entertaining. And when it wants to be good, it can be really good. I think the personal favourite is the last season, which, in my opinion, is pretty much perfect in every way.
1. FMA (2003 version)
I'll keep this short. Love the way they handled the original source material and turned into a story of its own. This show is incredibly mature, has great characters, amazing music and art style and plot twists that are well hinted throughout the series. And the ending, both the show and the movie, follow the morals of the story and in a way, leave you bittersweet but satisfied with the result.