[manyhats]

The least costly line I know of is Pullmantur. Their repositioning cruises across the Atlantic are frequently under $50/day for a solo passenger.

US$37 / day at current exchange rates and including taxes and semi-obligatory gratuities: http://www.pullmantur.com.br/pt/cruzeiros/-/cruzeiros/posici...

US$39 / day: http://www.pullmantur.com.br/pt/cruzeiros/-/cruzeiros/transa...

Heads-up: English is not the primary language of most passengers, but from what I've read, the crew can accommodate it.

Norwegian also has some that are under $100/day including taxes and gratuities. The one below is $968.95 for 13 days ($75/day), assuming you take the promo where the cruise line pays for the gratuities.

http://www.ncl.com/cruises/STAR13DVRPDLMIATPA?itineraryCode=...

(click all the way through to the final pricing page - the first page isn't what you get charged)