The two main Backpacker hostels that everyone seems to drift to, are located across the road from one another on Granville Street, the main entertainment strip (bars, clubs & restaurants) in town. They are:
The Samesun: http://is.gd/Ss7cpk
HI Vancouver Central: http://is.gd/ajlpeP
These are well and good for the fact that you are smack bang in the heart of town where it all happens, but this can mean a LOT of noise pollution at night too.
A quieter option not that much further away from Granville Street is:
HI Vancouver Downtown: http://is.gd/uDvMha
These are probably your 3 most popular hostel locations. about 9 years ago