Summer 2016: If you want to allow purchasing memberships / subscriptions online, also see Membership / Subscription Sign-up & Pay Online
If enabled, users can sign up and create their own account. These accounts will automatically be given a "request" (aka account request) membership type defined in your Organization Settings.
By default, the "request" membership type does not allow rental or check-out of items (though you can change this). This is to allow your organization to ensure the user, if they signed up themself online, fills out any required paperwork or agreements before you loan or rent items to them.
If you find there are large number of "request" users in the system, this may mean you have set your "Self Registration Membership Type" to be the same type as your "Default Membership Type" or another "approved" type.
To enable self registration, go to:
Settings -> Organization -> Edit Organization and make sure "Allow self registration" is checked off: