Proof Sets
The U.S. Mint produces proof sets of coins that are in circulation annually. The also produce mint sets, which are uncirculated coins that will appear in general circulation. Since the 1970s, both proof and mint sets have been encased in plastic to provide protection. In the earlier sets (through the early 1960s), sealed plastic was used on these special coin sets, but this was not as airtight as the encased plastic.
Presidential Dollars
Beginning in 2007, the U.S. Mint started releasing Presidential dollar coins, at the rate of four per year. The Mint also instituted a Presidential Spouse coin for each President, though these are sold separately and not in general circulation. The proof Presidential dollars are encapsulated in plastic, with all four Presidents included for collectors and coin sellers. Moreover, should either a Presidential coin or Spouse coin increase in value (beyond its face value), it would be encased in plastic by one of the two most recognized coin grading services: Numismatic Guarantee Corporation (NGC) and Professional Coin Grading Service (PCGS).
Commemorative Coins
Commemorative coins are produced to honor or memorialize a certain place, even or person. Commemorative coins are not placed in general circulation. The U.S. Mint produces its share of commemorative coins, but in 2011, England's Royal Mint produced a special coin for the royal wedding of Prince William and Princess Catherine. The "wedding coins" were minted within a week of the royal festivities. In the U.S., the Presidential Spouse dollars are purely commemorative. To preserve the as-new appearance of such coins, and to protect any investment value they may have, collectors encapsulate these coins in plastic.
Professional Coin Grading
Among the coin collecting public, there is a huge business in trading coins. Grading is the way to establish the physical condition of a coin. Numismatic Guaranty Corp. and Professional Coin Grading Service are among the recognized grading services. Companies in this industry grade any coins submitted to them. Both as a matter of record, and to preserve the coin "as is" when it is graded, these firms place the coins inside a plastic core piece, which secures it within the transparent holder. The shell pieces are encapsulated through a combination of compression and ultrasonic vibration.