1. Cowboy Bebop
2. Trigun
3. Rahxephon

I like stories about emotionally-damaged characters that rise above their circumstances to become heroic. Not to mention that I really think you need to see the first two to understand what an anime classic looks and feels like when you view it. The last title is a very personal choice and reduced me to sniffles for a little while. All three will make you think about the value of life in a more profound way. This was tough because I completely left out some really good anime, but the list said three and I can damn well count

1. One Piece ( I hated it at first because everyone loved it. But it really lives up to its name)
2. Gintama ( Most all-rounded anime i've seen. Simply the best)
3. DRRR! (I really loved the opening song)

1. Now and Then, Here and There
2. Gurren Lagann
3. Kino's Journey

1.One Piece
2.Naruto
3.Bleach
4.Fairy Tail

1. One Piece
2. Fullmetal Alchemist
3. Gintama

1. Clannad

2. Toradora!

3. Melancholy of Haruhi Suzumiya

I'm a sucker for romances

death note
arakawa under the bridge
dragon balls

maybe sailor moon cause it's so old..

1. baccano

2. beck: mongolian chop squad

3. madoka magica

1. Cowboy Bebop
2. Baccano!
3. Death Note

1. One piece
2. Naruto
3. Death note

1. Naruto
2. Bleach
3. That one about pirates

Now, you might be wondering why I intentionally picked the three worst anime I could think of. Let me explain.

The reason I did this was because I don't want anime to become more popular or further polluted by the horrible tastes and disgusting fan culture of 13 year old middle-schooolers. If everyone knows about these horrible anime then they will have a first impression that anime is very horrible in general and will cease all relations with anime henceforth.

This will leave only the true fans such as myself to remain in obscurity enjoying an art form rather than a commercial product made to be enjoyed by tons of people.

Just compare the horrible trash that Disney makes with the artfully crafted creations of Kyoto Animation.
In Disney's case you have bland perpetually happy children's stories that are successful worldwide
In Kyoto Animation's case you have hidden gems telling some of the greatest stories ever crafted by mankind (K-On!!, Hyouka, Haruhi etc.)

1. Gurren Lagann

2. Madoka Magica

3. Deadman Wonderland

1. Eureka Seven

2. Seirei no Moribito

3. Spice and Wolf

This is a terrible idea, the more anime sells, the more risks the production companies will take. Thus, the more quality anime we will receive. Your idea would destroy the anime market completely, leaving only the big sellers and destroying any possibility of production companies making the masterpieces you want.

I've got two different lists.

One: for those who have very little experience with anime:

1) Cowboy Bebop
2) Tiger and Bunny
3) Planetes

Two: for those who are experienced with anime

1) Big Windup!
2) Kenichi the Mightiest Disciple
3) Princess Jellyfish