Like some others in this thread, I haven't actually bought much music that came out in 2003 (just three albums and an EP), and while I like most of it, I don't think anyone would call Venus Hum or The Lucksmiths the best (although the Lucksmiths "A Little Distraction" EP is quite good, I think).
But, I haven't been totally out of touch, hearing songs here and there that I've enjoyed almost enough to purchase the respective albums. (For what it's worth, I meant to get some of these last time I went shopping, but came away with selections from 1963-2001 instead). Thus, I present my list of ten releases that would probably have been my favorites it I'd gotten around to hearing them in their entirety:
Gotan Project - "La Revancha Del Tango"
Mojave 3 - "Spoon And Rafter"
Sun Kil Moon - "Ghosts Of The Great Highway"
Ugly Duckling - "Taste The Secret"
Black Rebel Motorcycle Club - "Take Them On, On Your Own"
New Pornographers - "Electric Version"
Basement Jaxx - "Kish Kash"
The Shins - "Chutes Too Narrow"
Dear John Letters - "Stories Of Our Lives"
Yo La Tengo - "Summer Sun"
Also a plug for my favorite radio station, KEXP, which is where I head all of this music. They stream live, if you're interested...