Those days are LONG since gone. In a modern age with insurance, customs and immigration rules, boats end up paying huge amounts to carry "human cargo". To legally work on a boat, you need union cards and about a million different certifications, each costing a pretty penny. Some cargo companies will take passenger, but the costs are often higher than those of actual cruise lines and much more expensive than flying.
Sites like CrewSeekers are private vessels looking for extra bodies. Most of them expect shared expenses, many will ask for certifications or experience. But every once and a while there are boats that just want company. It is very difficult to find someone going where you want to go when you want to go there. Be wary though, as a single female, the middle of the sea is not a secure place to be with a stranger.
Just looking at the LPs life on the ocean forum you'll see how many relies posts get. This is totally possible (i know people who have done it), but unlikely.