Here's what I've got so far:
The Grouse Grind:
No list of Vancouver hikes would be complete without this one. "Nature's Stairmaster" isn't that what they call it? Imagine walking up a mountain that's practically perpendicular to the ground. Sound fun? Well, I don't know if "fun" is the first word that comes to mind, but by the time you make it to the top you'll feel like you could do anything (maybe after a little nap). The path itself is only a few kilometres long, but it feels like a lot more due to the severe incline. If you're going for a lazy Sunday, admire-the-view kind of hike, go somewhere else.
More info here: http://www.grousemountain.com/Summer/summer-activities/vancouver-bc-hiking-trails-trips/grouse-grind.asp
Minnekhada Park
This park is gorgeous, and a good combination of admiring the views and getting a workout. The High Knoll path is steep, but not too long to handle, and from the top you get a great view of the Fraser Valley, Pitt Lake, Pitt Meadows, etc. It's gorgeous! This one is a bit further away, being in Port Coquitlam/Coquitlam.
More info here: http://www.greatervancouverparks.com/Minnekhada01.html
This list is by no means complete, and I plan on continuing to work on it, but if you have suggestions of great local hikes, send them to me or comment!