Here’s a picture from van der Linden, D., et al. (in press) [The General Factor of Personality: A meta-analysis of Big Five intercorrelations and a criterion-related validity study. Journal of Research in Personality.]:
(α is also more memorably called “Stability” and β is “Plasticity”; GFP is the General Factor in Personality.)
This suggests that, on self-reported questionnaire responses, openness and extraversion tend to go together, and that conscientiousness, agreeableness, and emotional stability tend to go together. Furthermore, all five tend to go together, e.g., pick a bunch of random extraverted people and, more likely than not, they’ll be agreeable and emotionally stable. Or at least they’ll report that they are so.
The authors allude to possible statistical artefacts causing the correlations, or factors of general social desirability.
The evidence for a “substantive” interpretation of the correlations comes from studies showing heritability of the general factor and correlations with other measures. The latter tend to be low, e.g., on average rs around .15, peaking at .3, between the factor scores and boss-reports of various factors of job performance.
What’s missing: explanations from the perspective of social and neural process theories.