We use Benny's last time we moved: http://www.bennysmoving.com/

What I remember most about them is that the movers were these lean and wiry types who carried everything in and out, up and down stairs. Nothing went on a dolly or cart. I remember at one point two men were standing in our driveway holding a refrigerator between them while carrying on a conversation with their boss about the precise location to place it. ("It's all in the grip," they said to me.) They made everything look so easy, and no walls were ever bumped even though our stairs are narrow and twisty.