Define a $good~word$ as a sequence of letters that consists only of the letters $A,$ $B,$ and $C$ $-$ some of these letters may not appear in the sequence $-$ and in which $A$ is never immediately followed by $B,$ $B$ is never immediately followed by $C,$ and $C$ is never immediately followed by $A.$ How many seven-letter good words are there?
1. **Define the problem constraints**: We need to count the number of seven-letter sequences (good words) using the letters \(A\), \(B\), and \(C\) such that:
   - \(A\) is never immediately followed by \(B\),
   - \(B\) is never immediately followed by \(C\),
   - \(C\) is never immediately followed by \(A\).

2. **Consider the first letter**: The first letter of the sequence can be \(A\), \(B\), or \(C\). This gives us 3 choices for the first letter.

3. **Determine the choices for subsequent letters**:
   - If the first letter is \(A\), the next letter can be either \(A\) or \(C\) (2 choices).
   - If the first letter is \(B\), the next letter can be either \(A\) or \(B\) (2 choices).
   - If the first letter is \(C\), the next letter can be either \(B\) or \(C\) (2 choices).

4. **Generalize for the remaining letters**: For each subsequent letter, the choice depends on the previous letter:
   - If the previous letter is \(A\), the next letter can be either \(A\) or \(C\) (2 choices).
   - If the previous letter is \(B\), the next letter can be either \(A\) or \(B\) (2 choices).
   - If the previous letter is \(C\), the next letter can be either \(B\) or \(C\) (2 choices).

5. **Calculate the total number of sequences**:
   - For the first letter, we have 3 choices.
   - For each of the remaining 6 letters, we have 2 choices.

   Therefore, the total number of good words is:
   \[
   3 \times 2^6 = 3 \times 64 = 192
   \]

Conclusion:
\[
\boxed{192}
\]