Is it ok to correlate before-and-after data? I am asked to draw a scatterplot and to compute a correlation coefficient for the following situation. A group of subjects are measured for a blood characteristic before and after surgery.
Is it OK to correlate before-and-after data?
I know that it is not OK to perform correlations on non independent data. I feel this is such a case--the two measurements are made on the same subjects--they should be correlated. 
I know that correlating data to the change over time is not OK--but that is obvious and it is not the case here.
Also correlating two variables measured repeatedly on the same sample is a huge No. But again it is not my case.
 A: None of those correlations you think aren't OK really aren't OK. The correlation is just a measure of linear relationship. Sometimes you need to know the extent of a relationship that you know exists, such as this one, or any of the others you listed. In this case they may want to know the amount of correlation for a variety of reasons ranging from needing it for a repeated measures t-test report to checking to see that the data are sound.
Perhaps what you mean by not OK is that it's not OK to examine such a correlation with a hypothesis test where the null is a 0 correlation. That wouldn't be OK because you know that there has to be some. But that's not what you're asked to do. 
A: This is perfectly fine. You are considering two different variables each measured once per subject. One contains the 'pre' values, the other the 'post' values. I think you are mixing up independence between observations (subjects) and independence of variables.
Please note that in your situation, you might want to analyze differences between pre and post, not just looking at correlations, depending on the scientific question.
A: I think it depends on what you are trying to do with your data. Technically, it is okay to correlate repeated measures from the same subject in the sense that it is mathematically possible. But if you trying to draw some kind of inference (for example, causality) from your data, simply correlated two observations that are from the same subject is not going to tell you anything useful.
Here's a nice little thread talking about correlations of repeated measures within subjects.
