Is the model wrong if a coefficient changes from minus in correlation table to plus in OLS? Perhaps a very basic question but one that has me confused. Say, in a correlation table the relationship between A and the DV (B) is .351, but -.150 in the OLS model (where you have added C, D and E variables), what does this then mean? In other words: if the C to E variables not only change the coefficient of A but even make it go from negative to positive, does that indicate an undesirable interaction effect between the variables used in the OLS? I have been checking the VIF scores for this but based on low VIF I have no reason to fear multicollinearity. What (if anything) is wrong?
I'm trying to wrap my head around this constructing a simple example for myself to understand. Say A is a person's height and B is the distance this person jumps. There probably is a positive correlation (higher means longer legs, means longer distance jumping). What variables C to E would offset this person's height, even to the extent that this person's height is working against him when jumping (making the coefficient between A and DV B in the OLS negative)?
 A: In addition to looking at the coefficients, you should also look at their confidence intervals.  If the interval is quite wide then a change from $0.351$ to $-0.150$ could be explained by random chance.  Even if the intervals are narrow (and show significant difference) a change in sign is not uncommon.
Remember that the interpretation of a single slope is the effect of changing that variable while holding all others constant.  Even with moderate correlation (well below the level that would cause a VIF to be interesting) this can be an unreasonable assumption that does not help with interpretation and can lead to the reversal.  Think of what it means to increase someone's height while keeping their weight constant.
Another example.  $Y$ is the value of all the coins in a person's pocket, $X_1$ is the total number of coins, $X_2$ is the number of coins in the pocket that are not quarters (or the highest common denomination of coin for the region).  We would expect positive correlation between all 3 variables, but if we hold $X_1$ constant and increase $X_2$ then $Y$ would decrease.
