Favorite band, hands down:
Coheed and Cambria
They are a progressive rock "concept" band. They albums are each a story in a singular over arching world. The story is called "The Amory Wars" and there are comics available by the same name. The comics tell the same story the albums do.
Most people know their song "Welcome Home". Some know "The Suffering" or "A Favor House Atlantic," but it's rare that they know more than that, if even that. I recommend listening to "A Favor House Atlantic" "Junesong Provision" and "Away We Go"
I don't know if they will draw you into the band, or away, they are just songs I enjoy. To be completely honest, in the 7 albums they've released, it's rare I skip a track.
Other bands/groups/people I enjoy (incomplete list, and in no particular order):
Placebo
Stromae
Die Antwoord
Daft Punk
The Knife
David Bowie
The Prize Fighter Inferno
Mika
Explosions in the Sky
Signal Hill
Bowling for Soup
October Project
Toybox