I just recently moved from Seattle to Tempe, Arizona and used Pacific Movers, which is the local Seattle branch of Wheaton Movers, and I cannot recommend them highly enough. Even though it's a large company, every step of the way felt local and family owned.
Kevin Smith came to do the estimate. He stayed for about an hour was really thorough and helpful in answering all my questions. Don Moe was the driver (his wife took inventory) and picked up my stuff with a couple of guys. Everyone was really nice and professional and super efficient--even the dispatcher was really helpful when I misplaced Don's number and wanted to confirm arrival time.
I lived in my one bedroom apartment for six years of grad school and had accumulated a lot of stuff--books and wedding presents especially. They picked it all up in exactly an hour and a half, and when they delivered it they put everything back together that had been taken apart and were done in about two and a half hours.
The total came to about $3700 which was a few hundred lower than the estimate itself--probably because I got rid of a bunch of stuff just before the move, which leads me to believe that the estimate itself was pretty darn accurate. I'm ashamed to say that I didn't get it together early enough to get more estimates, though my experience with Kevin left me trusting him.
The only down side was that they allocate two days that they might come to pick up and same for the drop off, though they confirm 24 hours in advance and then stick to it. Also, I had to wait a week and a half for my stuff which was a bit on the long side, but I was the first pick up and the last drop off so I guess that's to be expected. They were really good about calling to confirm the day before exactly when they'd be arriving and then getting there within minutes of the time they quoted, though.
Although the time windows were a little annoying, it struck me more as a matter of honesty about when they could actually come unlike some stories I've heard where they'll set up a definite appointment and then flake at the last minute. So anyway, I'd definitely use them again.
Oh, and one more thing--because of Seattle city ordinances that don't allow really large trailers to park in the city, there was an extra charge for the shuttle that they had to bring in, but they were up front about that and there were no extra fees or hidden charges. And they take care of arrangements with the city to block off parking spaces and stuff like that.