The BC Ferries website FAQ suggests that there aren't any scheduled ones running at the moment:
Q: Do you have a ferry that travels between Seattle and Vancouver?
A: BC Ferries does not provide service between Seattle and Vancouver, and we are unaware of any companies that do at this time.
I think the issue is that it wouldn't be popular enough for a direct service. Most people wanting to travel that route direct will do one of drive, take the bus, or take the Amtrak Cascades Train (which is supposed to have great views).
What there are is quite a lot of people in either Seattle or Vancouver who want to visit Victoria and the rest of Vancouver Island. I think your only option is to change ferries there. It's supposed to be a very nice spot to visit, so you could maybe even stop off for a day on your way. You've even got the option to take the ferry to one part of the island, make your way along, then continue from a different port. There seems to be a good map of the ferries on the Vancouver Island website. If you're feeling really keen, you could even stop off on both Vancouver Island, and one of the San Juan Islands. (I've visited the latter, which was nice AND we can got to see whales on the trip! I've not yet been to Vancouver Island, so I can't comment on that yet, will hopefully update this bit in late June when I have!)
Oh, and just so you don't get false hope, Clipper Vacations (who run ferries between Seattle, the San Juan Islands and Victoria) will sell you tickets between Seattle and Vancouver, but these are actually for the train or the bus, not a boat