To evaluate \( 1001^2 - 1 \), we can use the difference of squares formula:
\[ a^2 - b^2 = (a - b)(a + b) \]
In this case, we can let \( a = 1001 \) and \( b = 1 \):
\[ 1001^2 - 1^2 = (1001 - 1)(1001 + 1) = (1000)(1002) \]
Now, we can calculate the product:
\[ 1000 \times 1002 = 1002000 \]
Thus, the value of \( 1001^2 - 1 \) is
\[ \boxed{1002000} \]