Correlation between BIS and BAS responses As a part of my lab experiment, participants had to answer questions for BIS and BAS (BAS reward, drive and fun) scales. The correlation matrix shows that BIS is significantly positively correlated with BAS reward, BAS fun and BAS drive. Has anyone experienced similar issues? Is this an issue? If yes, is it possible (and how) to correct for that?
BIS (Behavioral Inhibition System) and BAS (Behavioral Activation System) - I administered the scale developed by Carver and White (1994), as presented on pg. 323 in their work "Behavioral inhibition, behavioral activation, and affective responses to impending reward and punishment: The BIS/BAS scales" (Journal of Personality and Social Psychology, 67, 319-333). I would assume that BIS should not be positively correlated with any of the BAS scales as BIS is related to avoidance motivation and BAS is related to approach motivation.I.e. a person scoring high on BIS should not be scoring high on BAS measures and vice versa. 
The variables are intended as predictors. I want to examine if BAS (approach motivation) sensitivity predicts a rightward bias in product choice, and if BIS (avoidance motivation) sensitivity predicts a leftward bias.
I haven't used BIS and BAS scales in my research, so I will only point out some general considerations.

Correctness of your correlation analyses.: Double-check your data analysis. Maybe you missed a sign somewhere or you didn't encode some scale correctly.

Interpretation of your correlation analyses. Significant correlation isn't that interesting. You should consider its magnitude. Note that the correlation between two measures is bound by the reliability of those measures. You should compare your correlation estimate with the upper bound and ask how much of the potentially available correlation it explains. In theory, the correlation can't exceed $\sqrt{r_a r_b}$, where $r_i$ is the reliability of measure $i$. (Carver and White provide the reliability estimates on page 323.) In practice this can happen due to measurement error and you should consider the confidence interval of your correlation estimate.

Measurement error or Systematic bias? On page 323 Carver and White (1994) write:


  In theory, the sensitivity of the BIS and BAS physiological systems
  should be independent. Consistent with this assumption, the BIS scale
  was relatively independent of the BAS subscales in this sample,
  although the degree of independence varied across subscales. The BIS
  scale correlated -.12 with Drive, .28 with Reward Responsiveness, and
  -.08 with Fun Seeking.


You should compare these values with your correlation estimates and ask whether your estimates are consistent with those of Carver and White. Again, confidence intervals may be helpful.

Regression with correlated predictors. Wikipedia explains why linear regression requires independent predictors and has (under Lack of multicolinearity) some suggestions for situations when independence can't be assumed. In addation you may want to look at this question on cross validated SE.