The answer is $\boxed{\text{C}}$.
The missing number is the number that completes the sequence. The sequence is a list of numbers that follow a certain pattern. In this case, the pattern is that each number is the sum of the two numbers before it. So, the first number is 1, the second number is 1 + 1 = 2, the third number is 2 + 1 = 3, and so on. The missing number is the number that comes after 3. To find the missing number, we add 3 and 2 to get 5. Therefore, the missing number is $\boxed{5}$.
Option A is incorrect because 4 is not the sum of the two numbers before it. Option B is incorrect because 8 is not the sum of the two numbers before it. Option D is incorrect because 2 is not the sum of the two numbers before it.