The Indian Cent (designed by James Longacre) was first minted in 1859 with a copper-nickel metal content, but no shield on the reverse. The metal content remained the same as the 1859 from 1860-1864, but a shield was added to the reverse of the coin.
The metal content was changed to 95% copper and 5% Zinc from 1864-1909, and the design remained unchanged. The lone exception is the 1864 Bronze (95% copper and 5% zinc/tin) and this date has a variety known as 1864 L, with the L representing the designer's initials. All coins where minted at the Philadelphia Mint and have no mint mark except for the 1908-S and 1909-S, which are the only dates struck in the San Francisco Mint.
The Indian Cent varieties are numerous and the above list should not be considered complete. One should always look for doubling of design features, repunched dates, over dates, die clashes, misplaced dates, etc. of which may signal a "variety" find.
Indian Head Cents came in rolls of 50 and it's very difficult to find an original roll of solid dates, but they do still come to market sometimes. You're more likely to see mixed date rolls of circulated coins.