Sorry for my bad english XD
I cried front of a lot of anime like : Air TV, Akame ga kill, AnoHana, Ayashi no Ceres, Clannad, Fruit Basket, Gosick, Kyoshiro to towa no sora, SaishÃ» heiki kanojo, Nagi no Asukara, Natsuyuki Rendez-vous, Shigatsu wa kimi no uso (lot of tears), Shingetsutan Tsuikihime, Soredemo Sekai wa Utsukushii, Ansatsu KyÃ´shitsu, Boku dake ga inai machi, ChÃ»nibyÃ´ demo koi ga shitai, Soul eater and Toradora! Certainly I have forgotten some of anime XD
I think, songs are important in a anime because, give us more emotions and japanese'svoices are incredible too!!