It’s not on the cards at the moment, and neither would it make much sense either.
From time to time, people start “chain updates” on Facebook in order to panic people. The messages basically say that Facebook will soon start charging users to access the website and all associated services.
The idea of these messages is to scare people into thinking that Facebook may be taken away from them unless they decided to pay. Sometimes the messages ask users to join a page or click through to a website. You should do neither.
The chances are that Facebook will never change the website to a subscription only service. Doing so would immediately cut the number of active users drastically, which would hurt Facebook’s only current revenue stream; advertising.
Advertising is one of the only ways that Facebook actually generates money. Companies will pay huge amounts of money to advertise on Facebook because of the sheer volume of users that it has. If it doesn’t have the users then companies won’t want to advertise on Facebook anymore and they’ll lose more money than they could ever make from a subscription based service.
So, short answer: No, Facebook will not charge people to use their service.