A lot of great songs on here already, but I figured to add a few that I think are worthy that haven't been mentioned yet
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From Inuyasha:
ED01 - "My Will" by Dream
ED02 - "Fukai Mori" by Do As Infinity
Inuyasha was one of my first experiences with anime after finding out what anime was, back when it was on the adult swim lineup. (I'd watched other shows earlier without really knowing what they were) I've always liked both of these songs I find myself listening to them often.
From Honey and Clover:
OP01 - "Dramatic" by YUKI
ED01 - "Waltz" by SuneoHair
Honey and Clover is one of my all time favorite anime, and the music is amazing and complements the show well.
From Cross Game:
ED01 - Koi Kogarete Mita Yume (恋焦がれて見た夢)" by Ayaka
(I couldn't find just the ending sequence, so here's just the full song)
This is just a really moving song and fits the show really well. Anybody who has seen the first episode of Cross Game should know just how powerful it is. It's a great example of how to use a song in an anime. That said, you should try watching ep 1 before searching for the song itself since it might involve a pretty important spoiler.