Seattle, USA:
The Quick Shuttle:
www.quickcoach.com
This is a coach service between Seattle and Vancouver with stops along the way. Be prepared for approximately a 4-hour journey and occasionally a long wait at customs, as each passenger must be processed individually. The website contains schedule and rate information. Hotel pick-ups are offered from most major downtown Hotels.
Updated info...
I have used quick shuttle many times and have to say this is the easiest way to get from Seatac airport or Bellingham airport to Vancouver without a car. The bus will pick you up right outside baggage claim and drop you at the cruise port. No cabs and fussing around at all.
Heading South to Bellingham/Seattle...
There are 2 ways this might be done - if you have just gotten off the cruise ship and the entire bus is ONLY cruise ship passengers, the bus will pull up and no one has to get off at customs. Since you have technically just gone through customs, they just let you stay on the bus and do a quick check.
Now if you are on the bus with non-cruise ship passengers, the driver will take all the luggage off the bus and place it outside the building. A dog sniffs it all and then you get off the bus, grab your own luggage and proceed inside. This is where you will have your passport out and customs card they give you on the bus to fill out. After you go through, you have to place your own luggage and all other items on the xray machine, and then once cleared, you can take it back out to the bus. There are washrooms in this building too that you can use.
It takes about 20-30 mins total.