Although I would't directly refer to Vrankrijk as sleazy, it is certainly an alternative bar that needs to be recommended on this site.
Vrankrijk is an old squatters place, that exists already for twenty years. Ten years ago the building was legally obtained, and last year they received a true permit for serving alcohol (although they were doing it already for twenty years).
Drinks are very cheap in Vrankrijk. However they don't always stay open late. Atmosphere is very good. On Saturdays you can dance a bit. Besides that there are lots of activities, and benefit nights.
Unfortunately most squatting places have disappeared in Amsterdam. Lets hope Vrankrijk stays!
Update: Unfortunately Vrankrijk was permanently closed in 2009 by the City of Amsterdam.