Well, we already know from another topic that the OP loves the Killers and Snow Patrol. And the Killers and Snow Patrol.
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Ugh. The Killers are fun, but Snow Patrol has to be one of the worst bands in the world. In fact, they feature in my favorite anecdote about bad music:
I was in the waiting room at St Vincent's low-cost psychiatry clinic in the West Village. It was a terrible morning, and I was miserable (hence, being in the psych clinic). There were a few people in the waiting room, including a very distraught young man insisting that if he didn't see someone soon he was going to kill himself. He would get up and start ranting every few minutes, while the security guard looked on cautiously and the receptionist struggled to keep him calm, the wait was long, however, and at the point when a social worker came out to announce that the wait to see a psychiatrist for walk in patients would be another three hours, the young man lost it and snatched the receptionist's phone to call his mother.
In the meantime I was sitting uncomfortably on bland and teared waiting room furniture, listening as soft rock was piped through the badly decorated clinic. As Snow Patrol came on I thought to myself that there could be no worse possible music to play in a low-cost psychiatry clinic waiting room. I mean, if anything is going to make you suicidal, Snow Patrol is it.
As I was thinking this the young man was screaming to his mother on the phone, "They want me to kill myself! They're telling me to kill myself!" and as he was screaming, Cher came on the radio singing "Do You Believe In Life After Love", and the young man screamed, "...and they're playing this music! They're playing this music to make me kill myself!"
I know it's wrong, but I laughed at how right I was!
Anyway, as to the question, disregarding single artists and focusing on bands, I love:
Belle and Sebastian
Asobi Seksu
The Decemberists
Nick Cave and the Bad Seeds
The Jesus and Mary Chain
Hot Chip
New Order
REM
Modest Mouse
The National
Pearl Jam
The Proclaimers
Slowdive
The Stone Roses
The Smiths