I guess this thread flew under the radar for me somehow. :huh: Well, they late is better than never! 
Going off of my favorite American bands, my #1 favorite of all time (and probably will stay that way) is Boston. This band was a favorite of my father and his siblings as well, so I have heard, and he would always let me borrow their “Greatest Hits” CD when I wanted to listen to it. I am not too well versed in the band itself or their history, but all I know is that I love their sound, have my own CD now, and will every once in a while throw myself back into it to have a good time. :laugh:
[spoiler]I am finding it impossible to pick a favorite song for them, so I will just not. 
Though, I will put Peace of Mind here as an example.
[video]http://www.youtube.com/watch?v=Ek8ejHBZ1uo[/video]
http://youtu.be/Ek8ejHBZ1uo
You should listen to all of their songs, though. :silly: [/spoiler]
When it comes to other American bands and singers, I rarely place them in any definable lists or orders. I do very much enjoy Billy Joel and Elton John (who I keep confusing with each other :S ), and would consider them favorites of mine as well.
I probably have forgotten a whole slew of them, but I guess I can always come back and add them in later. ^-^;
Just a quick Elton John favorite known as Your Song. :3
[video]http://www.youtube.com/watch?v=13GD78Bmo8s[/video]
http://youtu.be/13GD78Bmo8s
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Then comes my list of favorite foreign bands; which, surprisingly enough, is dominated by Japanese artists (imagine that :lol: ).
There are so many artists that I could name off that have made it into my “favorites” category, but among all of them, I would say that Yoeko Kurahashi (倉橋ヨエコ) is at the top of my list. Even if I cannot understand half of what she is singing (and only understand the other half through possibly faux translations), her sound and the overall emotion she puts into her voice just makes me love it no matter what she ends up singing. And if any of the translations are to be trusted, the messages and stories she puts into her songs are absolute magic. B)
Out of all of her songs, I like this one the most; mainly because of its message.
The English title is called Raining Again Today.
[video]http://www.youtube.com/watch?v=xPzK_ce1fgg[/video]
http://youtu.be/xPzK_ce1fgg
Another Japanese band, comprised of three singers and known as Perfume (パヒューム), has made it into my favorites as well. I originally heard them first when I was playing http://osu.ppy.sh/, and they slowly began to grow on me. There will be times when I am not in the mood for some of their songs, but there is always one that will get me smiling every time. :side:
One of their songs that I know I will most certainly get a smile from is Kokoro no Sports.
[video]http://www.youtube.com/watch?v=FS7GEt_BHqM[/video]
http://youtu.be/FS7GEt_BHqM
Dipping more into the anime scene, I would have to say my favorite band that ever added to an anime’s soundtrack (which is getting a run for its money by the Seatbelts (シートベルツ)) would have to be The Pillows (ザ・ピロウズ). Most known by their work on FLCL, The Pillows became a long-lasting favorite of mine.
Here is one of their songs that got me into the strange (and seemingly foolish) habit of referring to them as the Japanese Beatles; Hybrid Rainbow.
[video]http://www.youtube.com/watch?v=bWIrPL4IhZ0[/video]
http://youtu.be/bWIrPL4IhZ0
And last, but most certainly not least, comes my favorite Touhou band of all time: Buta-Otome (豚乙女). The whole band’s line-up seems to impress me every time I hear a new song, or even an old one I had not heard in a while. I love this band so much, and even enjoy listening to their non-Touhou material to my heart’s content. Ranko (ランコ), their vocalist, is the crown jewel in this euphoric conglomeration of exceptional talent. Their sound, their lyrics, their feeling (even if I do not know a word they are saying). I love Buta-Otome, and I love Ranko; and it seems that many other circles love her as well, seeing how she appears in so many other circles’ releases. I could go on for days about how much I love this band, but I think this is enough. 
For this band, I cannot possibly find any way to post one song over the other as far as favorites goes, so I will simply put the first song I ever heard: Fantasy Satellite (幻想のサテライト)
[video]http://www.youtube.com/watch?v=7KCse6HDu08[/video]
http://youtu.be/7KCse6HDu08
Sorry about the SUPER long post here, but I felt as though I had to include all of these or it would not be fair (however odd that may sound when I actually put it down :dry: ). I hope I did not go overboard. :whistle: