Yes, kind of...
Yes, it is "fine." See this 10-case example, where case 5 and case 7 both have a missing:
Now, look at their correlation outcome, there are only 8 cases participating.
The reason is that Pearson's correlation requires the covariance between $x1$ and $x2$ to be calculated. If either one has a missing, there will be no covariance resulted, and the case is thrown out.
Now, to further illustrate, let us use select case to filter out the two cases:
And rerun the correlation again, the results are identical. This exclusion does not just happen to system missing, if you have assigned a user-defined missing, the case with that user-defined missing will also be excluded.
I said that it's "fine" because it's true that SPSS does screen out incomplete cases for you. But it is in no way solving the missing phenomenon for you. If there is any systematic reason that causes your participants to not answer a certain question, you correlation coefficient can be wrong. However, if you feel that they missed the answer in a random manner, then your correlation shouldn't be heavily affected, though you may lose some sample size and consequently power.
Q: But - I ask you - please tell Tania about pairwise and listwise deletion of missings and under what button it is found in SPSS -- ttnphns
A: Certainly. It would be necessary to illustrate with another example in which we have a new candidate, $x3$:
SPSS correlation analysis uses pairwise deletion by default, which means it'd always maximize the number of case in each of the pairwise comparisons. We have learned from above that the correlation between $x1$ and $x2$ has a sample size of 8 pairs. What about $x1$ and $x3$?
Turned out, it's 9 because maximally there are 9 pairs of data. Now, this can get inconvenient if you'd like to screen off the whole case and prevent it from being analyzed. In that case, you'll use list-wise deletion.
To call the option up, in the Correlation menu, press
Option and then check
Exclude cases listwise, then press
OK to submit the test again:
Now let's run the correlation matrix again, you'll notice that all sample sizes are unified to 8; only cases that provide data to all the three variables are retained. Visit this IBM FAQ if you'd like to learn more about the two types of deletion.