The value of a 1972 Eisenhower dollar depends entirely on which version of the coin you have. The most significant factor is whether the coin contains silver, which is determined by the mint mark, a small letter indicating where it was made.
Most 1972 Eisenhower dollars were minted for general circulation in Philadelphia (no mint mark) and Denver (a "D" mint mark). These coins are made of a copper-nickel clad composition and contain no silver. Consequently, their value is typically just their face value of one dollar, unless they are in a very high, uncirculated grade or possess a rare error.
The valuable 1972 dollars were struck at the San Francisco Mint and bear an "S" mint mark. These coins were created specifically for collectors and are composed of 40% silver. They were sold in two finishes: an uncirculated version often found in a blue envelope ("Blue Ike") and a proof version sold in a brown box ("Brown Ike").
The base value for a 1972-S silver dollar is its silver melt value, which fluctuates with the market price of silver but is typically around $6 to $7. However, as collector's items, they are almost always worth more than their metal content. The specific value depends on the coin's condition, or grade. According to NGC, a typical uncirculated 1972-S silver dollar can be worth from $14 to $21. The value increases sharply with quality; a near-perfect example graded MS-69 could be worth as much as $375.
