I have a couple of other suggestions that are among my favorite spots to visit along with many of those on Vlad's great list.
First off would be Spanish Banks Beach Park, which is adjacent to the west of Jericho Beach Park visible at the left edge of Vlad's map. It gets you a bit closer and often at a better angle to the ships anchored in English Bay, and you also don't have to worry as much about the position of the sun.
Near Vlad's Point D, which is known as New Brighton Park, I would also recommend taking a walk or drive along Wall Street, as there are many pocket parks that also provide a view of ships moored and at anchor on the Burrard Inlet. Nearby, if you're up to a long walk, traversing the Steel Worker's Memorial Bridge can provide some interesting view, however suicide fences were recently installed, so it requires jockeying your camera through the fence posts to get any decent photos. Finding the parking to access the bridge also takes a bit of hunting.
For fishing boats, False Creek Fishermen's Harbour adjacent to 1st Avenue & Creekside Drive usually has a small contingent in a photogenic setting. Further out of town to the southwest, the town of Steveston, BC offers a larger fishing fleet, along with Garry Point Park, offering views of the cargo and tug traffic transiting the mouth of the Fraser River.
There are many other pockets that can net you one or two interesting vessels, but those are mostly difficult to find and out of the way. What had been mentioned so far is really the bulk of the valuable locations in and around Vancouver.
Kind Regards,
Kyle