I am not aware of how many social network services exist, but I am sure it must be hundreds if not more. Most of them operate on a "come in and find out" basis, which means that you sign up and have a look, and most often, you just stay registered, whether you really use the service or not.
Some of the services are restricted, i. e. they work on an invite-only basis. This may have the advantage that the newly registered user at least has one connection within the network if this person is invited by someone they know, but if any registered user is able to invite any other user, I do not understand what the benefit would be.
I have the impression that the networks that may prove to be the most useful to me are those where I can define what class of relationship links me to the person in question (e. g. family, friend, acquaintance, virtual contact), as it may be employed by application services built on top of a network managing service, e. g. in order to provide useful recommendations.