Here are some songs that have appeared in Inuyasha. Pick your favorites. I don't even watch Inuyasha but some of my favorite songs have come from the series. I only included the ones I know as options
dream - my will (1st ending)
Ayumi Hamasaki - Dearest (3rd ending)
BoA - Every Heart -Minna no Kimochi-(4th ending)
Hitomi Shimatani - ANGELUS (6th opening)
alan - Diamond (10th ending)
Ayumi Hamasaki - no more words (1st movie ending)