Factor dependent correlation If I take a set of measurements and test correlation of variable $A$ vs variable $B$ and get a significant correlation, that makes sense to me.  But what if further analysis reveals that of those factors, there is only a significant positive correlation within one group, and that group is over-represented.  Is the global correlation still valid, or is it, upon more detailed inspection a sample-bias effect?
Here is some graphs to explain:
The global correlation

The group separated correlations

 A: Are you familiar with Simpson's paradox? This would seem to be what you're observing here.
Edit: I didn't answer your question :) What exactly you should do is to some degree context dependent (Are the groups meaningful? Does this represent a problem in the study design? etc). At the very least you should report both results IMO.
A: I agree with JMS advice, that the answer is totally context dependent.
But what you are looking at may also be considered a moderation effect. 

In statistics, moderation occurs when
  the relationship between two variables
  depends on a third variable.  

(quoted from wikipedia)
A moderation is statistically significant if in a multiple regression analyses the interaction of the predictor with the third variable is significant.
A: The previous comments are all good, but with group sample sizes of 5, 7, and 11, I wouldn't trust any of their correlations as far as I could throw them.  You'll need to give the overall r a wide confidence interval as well.  btw Nice job on the graph.
