Can't believe we're on page 3 and I've not seen one mention of Leonard Cohen. Talk about distinctive.
Also, I'd say:
Tori Amos (I don't consider them to sound the same vocally AT ALL even though their songwriting style is similar)
I was gonna say Peter Gabriel until I remembered that I once mistook Steve Winwood for PG!
Andrew Eldritch (Sisters of Mercy)
As for those that send a shiver:
Lennon and Gabriel. STOP.