As far as I know, the only "vouchers" are section 8 vouchers with a couple sub-categories. As far as I know the waiting lists for these vouchers is TERMINALLY long.
But there are a lot of deals that don't involve vouchers if you qualify.
Start here:
NYC Affordable Housing Resource Center
(choose selection on left side.)
And here:
HPD - Apartment Seekers - Current Housing Lotteries
You can sign up for e-mail at the second site and they'lll notify you as each deal comes through and what the requirements are.
But forget vouchers, if you don't have one now, you won't get one.