Memberships are similar to subscriptions in that they generally require regular periodic payments. However many memberships are offered at no cost or at a nominal sum to customers. Usually the benefit to customers is that they get a number of points for each purchase made. The points accumulated can then be redeemed for vouchers with cash value that can be used to offset purchases.
Many financial institutions that issue your credit card operate a membership system at a nominal or no cost to you. For them, you receive points for every transaction that you make with your credit card, depending on the value. Besides the financial institutions, many retailers like supermarkets also issue memberships. The airline that you fly is another example. For flying with them, you receive certain number of air miles which can be redeemed for free flights or discounts.
However the memberships mentioned above are not considered serious income sources. By all means, introduce a membership system for your business if you think its beneficial even thought it does not directly generate much income.
The memberships that are serious income sources are more like subscriptions. An example is the membership of a Gym which allows for free unlimited usage of its facilities for a specified duration, usually a year. Memberships of theme parks where one gets unlimited entry for, say a year, for a fee is another worthwhile example.
You can have different tiers of memberships. An economy tier can allow for free usage or entry during non-peak hours. This tier can be attractive to those who wants the membership benefits but have more time than money. A gold or platinum membership is available where members pay a premium but have unlimited usage or entry at all times.
The advantages of memberships are similar to subcriptions. Thus memberships are a viable option especially for those providing services. However you have to make sure that customers perceive that they are getting good value for their memberships. Otherwise the renewal rate for members will not be high.