How profitable are websites that require paid memberships?
Congratulations on your new website!
Websites that offer paid memberships are actually pretty successful and profitable. Many evolve into full-blown online communities because of their success. There are hundreds of examples of these websites and communities. A quick Google search will reveal hundreds, but it's good to study the masters.
There is an art and science to running a successful membership-based website with much of it resting on the website owner's ability to provide content that the members will not be able to receive anywhere else. One membership website that's very successful is 5000 B.C. owned by Sean D'Souza: http://www.5000bc.com/.
Sean gets it right! Study him and you'll be well on your way.