Why by Ayaka. Zack Fair died to it, and that was damn sad to watch. It's just a very good song for "Yeah, I'm dying. This is emotional. Deal with it."
Other Possible Songs:
Why or Why Not (Katakiri Rekka): It seems like a song that'd play while someone dies, which is ironic because it's from the Higurashi anime. People died a lot in that anime. Though no one's really explained what the hell happened to Rena in the second ark....
The Price of Freedom (from Crisis Core): If I was to die fighting, this would be the song I'd want to go down with. It played in the final battle in Crisis Core (yes, I need to get off Crisis Core and move on) and it was just really sad. Most cry worthy battle in the world.
Dango Daikazoku (from Clannad): It seems so.... I can't describe it. You just feel so peaceful while listening to the song, and it feels like you're being sung to sleep. So if I were to slowly drift away into death, Dango Daikazoku would be the option for me.
That's enough for now.
