The shutdown will happen slowly over the next few months. If you're not already a member, you can sign up and start earning Coins until March 31st. Nintendo says that its New 3DS systems -- available next month -- will not earn Coins, although all other hardware and software will do.
North American members have until June 30th to spend their hard-earned Coins on whatever perks their interest (more physical and software reward options will be added over the coming months, so it might be worth waiting). In Europe, that date is extended to September 30th, and there are also slightly different rules about earnings and redeeming Coins that are worth checking out. Nintendo says a new-and-improved membership program is coming "later this year." Here's hoping it won't require filling out seven-page surveys in exchange for key rings.
Update: As pointed out by a couple of readers, in North America the reward system is based on "Coins," rather than the "Stars," "Star Points" and "Points" that the rest of the world collects. This article has been modified to reflect that fact.