AMV by Marissa Panaccio.
The song is 'Hall Om Mig' or 'Hold Me Now' by Nanne Grönvall. Lyrics can be found here: reewebs.com/hallommig
Many thanks to YouTuber flugansomintekomhem for the translation. :)
This AMV has awards for "Best Action" and "Best of Show" from Anime Boston and "Best Freeform" from Fanime.
Marissa's website can be found here: rwolfie.net/main1.htm
If you liked the video, you should definitely download the full-sized version from her site! It's much larger and clearer.