What animes are good to watch?

Well if 당신 are just beginning to watch 아니메 then i would suggest Fairy tail, Soul Eater, and Naruto. If not then i would recommend Attack on Titan, Code Geass, and Vampire Knight. Prince of 테니스 is also really good.

Fullmetal Alchemist Brotherhood
Fairy Tail
Sword Art Online

Dragon Ball Z, Yu Yu Hakusho, Inuyasha, and Kill La Kill

Hmm... well for a newbie, I'd recommend:
Death Note
Noragami
Psycho-Pass
Durarara (the one in the pic)

Though there's plenty of good 아니메 out there! ;)

I watch a range of animes so idk what your type is. But here are a few recommendations
Shoujo/Romance Comedy: Ouran high school host club, Kaichou wa maid-sama, Gekkan shoujou Nozaki-kun (a lot 더 많이 comedy than romance)
Slice of Life: Kimi to Boku, Anohana
Sports: Haikyuu!! (HIGHLY RECOMMENDED), Kuroko no Basket (some superhero like powers in there like "I have perfect shooting" 또는 "I'm almost invisible" "I'm a copycat i can copy anyone's moves")
Combat/Bloody/Battle: Fullmetal Alchemist (HIGHLY RECOMMENDED), Soul eater, Attack on Titan (HIGHLY RECOMMENDED), Naruto, Owari no Seraph
Slower animes that are NOT slice of life: Natsume Yuujinchou (HIGHLY RECOMMENDED), Mushishi, Kyoukai no Kanata
Music: Shigatsu wa kimi no uso
Other: 노라가미 (HIGHLY RECOMMENDED)