I've found the Toronto thread to be quite helpful, so I thought why not start one for the number one city in the world? And what better day for it than its 125th anniversary? I call on Vancouver-GAF to help make this OP a useful resource to anybody who wants to visit or move to Beautiful British Columbia =)
Public transportation is handled in Vancouver by Translink. Transit is actually pretty amazing in the Metro Vancouver area. We may complain about how late buses are sometimes and how little they run in some of the outer areas, but it's a pretty great system relatively speaking. The SkyTrain is the lifeline of the system and you will grow to love it if you use transit on a regular basis.
Both Google Maps and Bing Maps provide transit directions for Vancouver and you should use those over TransLink's site because TransLink is confusing.
The SkyTrain map can be found here. There are three lines in service. The Expo Line goes from Waterfront station in downtown Vancouver through the south part of Burnaby, New Westminister, and ends in Surrey. The Millenium Line follows the same path but splits off in New Westminister and loops through the north part of Burnaby instead of Surrey. The recent Canada Line takes riders from Waterfront to the city of Richmond which is where the Vancouver International Airport (YVR) is located.
How bad the buses are depends on where you live. Checking Google Maps / Bing Maps is your best bet on figuring out which to take. Night Buses go until 3AM and cover a good portion of the city!
The Seabus provides ferry service between Waterfront Station (Vancouver) and Lonsdale Quay (North Vancouver) every 15 / 30 minutes depending on the time of day.
Everything in this thread was outdated so I got rid of it all aside from transit. Special Thanks to my cousin for letting me use her beautiful picture of the False Creek area for the banner up top.