I had a lot of trouble finding a good video for this song. All the ones on YouTube were fan made ones that were rather poor. The one I have here is the best I could find from there. I strongly suggest you go ahead and skip to 0:24 on it when it starts. But hey, at least it has lyrics!
Again by YUI (http://youtu.be/-ye_EoVcODw)
I found this lovely song a few years back when it was topping the Japanese song charts and had been announced as the opening song for the anime Fullmetal Alchemist: Brotherhood (which is great :P). It was released in 2009 on YUI's fourth studio album and is actually her fourth number one single! It even sold over 95,000 copies in its first week!
I feel a little bad for sticking you with a pretty off video of her performing this great song. But not to worry, I dug around some more and found an official video! That is if you don't mind that its a Chinese website. ;P
Here's that link: (http://vlog.xuite.net/play/QWc3ZUgyLTIwMDIyMzQuZmx2/YUI-Again-PV)
More info: (http://en.wikipedia.org/wiki/Again_(Yui_song))
More info (for those curious) on Fullmetal Alchemist: (http://en.wikipedia.org/wiki/Fullmetal_Alchemist)