My Guide :
Classics :
- Full Metal Alchemist Brotherood (start with this one !)
- Saint Seya (action, kinda good)
- Naruto (Great Story overall, action)
- One piece (Funny and creative)
- Dragon Ball Z (Classic !)
- Card Captor Sakura (Reinvented Moe, inspiring all animes since then !)
- Sailor Moon (Inspired Card Captor Sakura, Yuri inside)
- Neon Genesis Evangelion (Launched the third wave of animation, GREAT !)
Modern :
- Haruhi (Slice of Life, launch the Light novel wave, awesome realisation overall) (Best narrator ever)
- Gundam Seed OR Gundam 00 (Where you need to start with gundam right now ! choose with your design taste) (Not childish as it seems)
- Puella Magi Madoka Magica (Surprise of the decade ! Adult, hard and cruel ! Best realisation !)
- Toradora (Best romantic Comedy)
- Candy Boy (Indie, twincest, cuter than hell !) (There are no boys, and it's not about candies either)
- Panty and Stocking (Japanese South Park)
- Sword Art Online (MMORPG, Virtual Reality, Bast Anime of 2013)
- Bakemonogatari (The books (novels) are awesome, shaft animation is as good ! A must see !)
- Ore no Imouto ga Konna ni Kawai wake ga Nai ! (Only if you like visual novels)
- Hourou Musuko (Adult (theme, not pr0n), talks about transvestism)
- Aoi Hana (Lesbian)
- Death Note (Shonen, nice)
- Digimon (If you still have you childish heart)
- Usagi Drop (adult theme, if you have childs, very interesting, I cried a little)
I probably forgot some. These are the best i could think off.