Now this is difficult to name just three...
If it were contemporary music and based on more than just one or two great songs, in other words a very strong catalogue: -
Sigur Rós
Mew
The Killers (if for nothing more than Hot Fuss)
Who the heck are Mew, Simon ??
They are an acquired taste

However, their album
Frengers was one of those rare CDs where, on first listen, I enjoyed every track. The 4th CD is very challenging but equally compelling once you have taken the time to actually listen to it.
You can read more about
Mew by clicking the link.