Interesting question...
Other than specialized clubs that cater to a single profession, the country clubs in my neck of the woods tend to attract a varied group. Lawyers, business executives, some doctors (although not all of them are in an income bracket where they can afford the fees...medicine is not as lucrative in Canada as it is in the U.S.), management consultants. I think the common element is that they're all in senior management somewhere, which gives them a sufficiently high salary to afford the fees.
The clubs I've been to usually have a golf course, swimming pool, tennis courts, fitness clubs or workout facilities, pretty grounds, often a restaurant, banquet hall, meeting rooms, party rooms, in some cases even accommodations. Many of them offer concierge services where they will get you tickets to events, deal with your dry cleaning, host dinner parties for you, etc.
In many cases, memberships are long-standing, passed from one generation of a family to another. For the clubs near me, typical initiation fees are about $75,000 to $90,000, and then there are annual fees of $15,000 to $20,000. Even if it's economically viable, it is awfully hard to justify dropping about $100K just to belong to a country club. That said, it can be a great environment in which to meet people, schmooze, discuss business in a less formal and structured environment, or just get out and play with friends.
Trinity