Off the top of my head one of my favorites come from Inuyasha and the song is called "Come" & I think it's by Namie Amuro... I get into every time I hear it... It is so soothing & up beat at the same time, plus the lyrics are not bad... It actually makes you want to "come/go with her"... lol ^_^
The song "Should I Love Him" was so emotional for me probably cause she sung the song with so much passion... It is by her also, but not an anime song...
Here is a link to the "Should I Love Him" <if anyone wants to listen> I am pretty sure everyone heard "Come", if they ever watched Inuyasha...
<Link>
YouTube - Namie Amuro- Should I Love Him
"Come" <Just in case you forgot>
YouTube - Namie Amuro-come
"Four Seasons" <Another good one from Inuyasha>
YouTube - Amuro Namie - Four Seasons
I have others, but that song right there was actually the first song that made me realizing I like anime music, so to speak... I will post more if I remember them & also thanks for making this thread cause I always wanted to know other artist/music, but didn't have the courage to ask, because I thought it was kinda of strange for me to like music that I don't know what they're saying beside the words in English <if any at all>... ^_^