My favorite band that never got any love in the US is the Hoodoo Gurus. They are a power pop band out of Australia. They range from straight punk with a tune like Be My Guru to more poppy stuff like Baby Can Dance or What's my Scene. Fantastic catalog of music.

Others that I love that get or got very little respect in the mainstream are Warren Zevon and John Hiatt as just brilliant song writers. I own just about everything Warren Zevon ever did including the obscure Hindu Love Gods album which has a great cover of Raspberry Beret from Prince. And John Hiatt has written so many famous songs, often for others. Come to think of it, so did Warren Zevon. Both never get the credit for the influence they have had.

And for absolutely the most obscure thing I listen too that is awesome is a woman names Anna Phoebe. Think of her as a progressive rock violinist. Reminds me of the huge productions one gets with Dream Theater or Savatage/TSO but no vocals, just violin. Her album "Rise of the Warrior" off of iTunes is phenomenal.

Although they're not some obscure artists, I still think they deserve much more recognition.

The Isley Brothers
Ray LaMontagne (although he did got a Grammy but that's about it)
Rose Cousins
Gregory Porter
Sara K
Chris Jones

Chris Rea
His stuff runs the range of brilliant, strange or just plain awful. But, his good stuff is absolutely fantastic. And, there's a lot of it to enjoy.

Steven Wilson comes to mind. Great music and sounds fantastic in 2 channel or multichannel. Not bad live either.
Joe Bonnamasa has some great guitar work. As previously said Warren Zevon, send lawyers guns and money.