The given inequality is:

$-2 < x < 3$

Since $x$ is an integer, it means $x$ must be a whole number between $-2$ and $3$, exclusive. The possible integer values for $x$ are:

$x = -1, 0, 1, 2$

Summary of possible values:

$\boxed{-1, 0, 1, 2}$

Would you like any further clarification or details?

Here are 5 related questions:

1. What would happen if $x$ were a real number instead of an integer?
2. How would the solution change if the inequality was $-2 \leq x \leq 3$?
3. Can you solve for $x$ if the inequality was $2 < x \leq 5$?
4. How would you represent this solution on a number line?
5. If the inequality was $-2 \leq x < 3$, what would the possible integer values be?

Tip: Always check the endpoints of inequalities to see if they are included or excluded in the solution!