Overall I recommend you to watch these Anime.

Some good highlight Anime:

• Baccano! (Action, Comedy, Historical, Supernatural)
• Berserk (Action, Adventure, Drama, Fantasy, Horror, Supernatural)
• Black Lagoon (Action)
• Cowboy Bebop (Action, Adventure, Comedy, Drama, Sci-Fi, Space, Bebop)
• Daily Lives of High School Boys (Comedy, School, Slice of Life)
• Darker Than Black (Action, Mystery, Sci-Fi, Super Power)
• Dennou Coil (Adventure, Comedy, Mystery, Drama, Sci-Fi)
• Ergo Proxy (Mystery, Sci-Fi, Psychological)
• Fate/Zero (Action, Fantasy, Supernatural)
• Gankutsuou (Mystery, Drama, Sci-Fi, Supernatural, Thriller)
• Ghost in the Shell: Stand Alone Complex (Action, Mecha, Sci-Fi, Military, Police)
• Golden Boy (Adventure, Comedy, Ecchi)
• Great Teacher Onizuka (Comedy, Drama, School, Slice of Life)
• Gungrave (Action, Drama, Sci-Fi, Super Power)
• Hajime no Ippo (Comedy, Drama, Sports)
• Hellsing Ultimate (Action, Horror, Vampire, Supernatural, Military)
• Hokuto no Ken (Action, Drama, Martial Arts, Sci-Fi)
• Hunter X Hunter (2011) (Action, Adventure, Super Power)
• JoJo's Bizarre Adventure (Action, Adventure, Supernatural)
• Katanagatari (Action, Adventure, Historical, Martial Arts)
• Kemonozume (Action, Demons, Horror, Romance, Supernatural)
• Kyousou Giga (Action, Fantasy, Supernatural)
• Legend of the Galactic Heroes (Drama, Sci-Fi, Space, Military)
• Macross (Action, Mecha, Music, Romance, Sci-Fi, Space, Military)
• Mahou Shoujo Lyrical Nanoha (Action, Comedy, Drama, Magic, Super Power, S2 is gold)
• Mahou Shoujo Madoka Magica (Drama, Magic, Psychological, Thriller)
• Mawaru Penguindrum (Comedy, Mystery, Drama, Psychological)
• Mobile Suit Gundam 00 (Action, Drama, Mecha, Sci-Fi, Military)
• Monogatari Series (Bake > Nise > Neko > Monogatari S2 > Hana > Tsuki)
• Monster (Mystery, Drama, Horror, Police, Psychological, Thriller)
• Mushishi (Adventure, Mystery, Fantasy, Supernatural)
• Neon Genesis Evangelion (if you want to watch it, pls ask me how you should watch it)
• Nichijou (Comedy, School, Slice of Life)
• Non Non Biyori (Comedy, School, Slice of Life)
• One Outs (Sports, Psychological)
• Outlaw Star (Action, Adventure, Comedy, Sci-Fi, Space)
• Paranoia Agent (Mystery, Drama, Supernatural, Police, Psychological, Thriller)
• Ping Pong The Animation (It´s not about the game, it´s about the people playing the game.)
• Princess Tutu (Comedy, Magic, Romance)
• Psycho Pass (Action, Sci-Fi, Police)
• Revolutionary Girl Utena (Drama, Fantasy, Psychological)
• Samurai Champloo (Adventure, Comedy, Samurai)
• Serial Experiments Lain (mind fuck warning, Mystery, Drama, Sci-Fi, Supernatural, Psychological)
• Shinsekai yori (Drama, Horror, Sci-Fi, Supernatural)
• Silver Spoon (Comedy, School, Slice of Life)
• Space Battleship Yamato 2199 (Action, Drama, Sci-Fi, Space, Military)
• Space☆Dandy (Comedy, Sci-Fi, Space)
• Spice and Wolf (Adventure, Fantasy, Romance)
• Steins;Gate (Sci-Fi, Thriller)
• Texhnolyze (Action, Drama, Sci-Fi, Psychological)
• The Melancholy of Haruhi Suzumiya (Comedy, Mystery, Parody, School, Sci-Fi, Slice of Life)
• The Tatami Galaxy (mind blow, Mystery, Romance, Psychological)
• Top wo Nerae! Gunbuster (Action, Comedy, Drama, Mecha, Sci-Fi, Military)
• Top wo Nerae 2! Diebuster (Action, Comedy, Mecha, Sci-Fi)
• Toradora (Comedy, Romance, School, Slice of Life)
• Trigun (Action, Comedy, Sci-Fi)
• Welcome to the N.H.K. (Comedy, Drama, Romance, Psychological)

Some good Anime-Movies:

• Akira (Action, Adventure, Horror, Sci-Fi, Supernatural, Military)
• Castle in the Sky (Adventure, Fantasy, Romance, Sci-Fi)
• Colorful (Drama, Slice of Life, Supernatural)
• Ghost in the Shell (Mecha, Sci-Fi, Police, Psychological)
• Grave of the Fireflies (Drama, Historical)
• Howl's Moving Castle (Adventure, Drama, Fantasy, Romance)
• Jin-Roh (Drama, Romance, Military, Police, Psychological)
• Kara no Kyoukai (Action, Mystery, Supernatural, Thriller)
• Memories (Drama, Horror, Sci-Fi, Psychological)
• Millennium Actress (Action, Adventure, Drama, Fantasy, Historical, Romance)
• Mind Game (Adventure, Comedy, Dementia, Romance, Psychological)
• Nausicaä (Adventure, Fantasy)
• Paprika (Mystery, Fantasy, Horror, Sci-Fi, Psychological, Thriller)
• Perfect Blue (Drama, Horror, Psychological)
• Princess Mononoke (Action, Adventure, Fantasy)
• Redline (Action, Cars, Sci-Fi, Sports)
• Saint☆Young Men (Comedy, Slice of Life)
• Spirited Away (Adventure, Drama, Romance, Supernatural)
• Summer Wars (Comedy, Sci-Fi)
• Sword of the Stranger (Action, Historical, Samurai)
• Tekkon Kinkreet (Adventure, Psychological)
• The Girl Who Leapt Through Time (Adventure, Drama, Romance, Sci-Fi)
• Tokyo Godfathers (Comedy, Drama)
• Wolf Children (Fantasy, Slice of Life)