1959 was the 50th anniversary of the Lincoln Cent, high time to make a design change. The front of the coin was left alone, but the reverse was changed from the old "Wheat Ears" design to a frontal view of the Lincoln Memorial. As a result, Lincoln appears twice on the new Cent: once on the obverse and second time as a tiny figure seated in the center of his Memorial (remember this, as it is the answer to a popular numismatic trivia question).
This is a lengthy series, with many interesting varieties, both major and minor. The rarest is the 1990-S No Mintmark, created when a worker at the Philadelphia mint failed to add the mintmark before shipping the die to San Francisco. The Doubled Die Obverse of 1972, the Doubled Die Reverse of 1983, and the Doubled Ear of 1984 are all popular, desirable, and valuable varieties. Close AM and Wide AM varieties have been found on a number of different years: sometimes, these are transitional differences, other times they are the usage of Proof dies to strike coins for circulation.
In 1982, the composition of the Cent was changed from bronze to copper-plated zinc; such pieces can be told apart easily by their weight. The older, bronze pieces are currently in demand because the value of the copper comes close to, or exceeds, the face value.
Building a set of Memorial Cents is easy and affordable IF the varieties are excluded. Most dates are readily available in Gem Mint State or Proof condition. Thus, this series makes an excellent starter set for new collectors.