I'll answer this one quite literally, as most of my favourite music comes from solo artists. Not many from people who play just on their own, but mainly from individuals who work under their own name - Joni Mitchell, Bruce Cockburn, Bill Frisell, Jonatha Brooke...
So my favourite band is probably The Blue Nile. They're a band I got into quite late. I'd bought an album, maybe even two, of theirs on Andrew Howie (AKA Calamateur)'s suggestion, but hadn't really listened much. But flipping through my iPod sitting in the car outside a post office somewhere in rural Ohio, Summer 2007, I put them on, for no apparent reason, and they got me. Hook, line and sinker, I fell for them. It all clicked. And I've been pretty much obsessed ever since.
They're an easy band to be into, as they've only released four albums in the 84 years they've been together (OK, 20-odd years, but it feels like more) - not very prolific. I'm always on the lookout for other projects that Paul Buchanan has been involved with, from producing Michael McDonald to solo tunes on compilation albums (I think I have a christmas song or two of his tucked away somewhere.
But as The Blue Nile, I love pretty much every note they've ever recorded. Which is exactly how it should be when every album takes 7 years to make :)