Only R.E.M. and The Monkees are on a par with Morrissey in my book as far as emotional, to-my-dying-day importance. But all of those artists are completely different from each other. It's like saying "if you could lose your arms, or your legs, or your eyes, what would you pick?" I couldn't imagine any of them missing from my life.
As far as repeat offenders go, I have massive love for Luke Haines, Aimee Mann, Michael Penn, Suede, The National, The Fall, Red House Painters, XTC, The Beatles, The Gaslight Anthem, Blur, early Radiohead, Springsteen, The Jam...
I went to a church bric and brack sale as a kid and found a 60's Monkee's annual with a signed photo from the band, dedicated to a fan.