How many personality factors are there?
The history of personality testing can be summarised in terms of an initial period where there was a vast number of personality traits. In response to this, there have been various attempts to synthesise these traits into a smaller number of underlying factors. There is a huge literature on this process (e.g., Digman, 1990; McCrae & John, 1992).
There are a lot of researchers who have proposed variations on the five factor model (commonly labeled OCEAN: openness, conscientiousness, extraversion agreeableness, and neuroticism). That said, you will find a range of other factorial models (e.g., Eysenk's three factor model; the HEXACO six factor model).
There has also been subsequent challenges to the resulting dominance of factorial models.
For example, see the research of Sampo Paunonen (e.g., Paunonen & Ashton, 2001) which suggests that we may have gone too far in embracing the factorial models of personality.
Related to this debate, there are a range of hiearchical theories of personality where facets are nested within factors. So you can either get a very general representation of personality with say 5 factors, and a more detailed representation with say 30 facets.
What are valid measures of these factors?
There are a large number of well validated personality tests.
Tests are typically built around particular representations of personality.
There are a range of free measures of the Big 5 listed here with some discussion around validity.
The NEO is one of the most well-known and used commercial measures of the Big 5. That said, there are a wide range of well validated commercial personality tests available.
References
- Digman, J. M. (1990). Personality structure: Emergence of the five-factor model. Annual review of psychology, 41(1), 417-440.
- McCrae, R. R., & John, O. P. (1992). An introduction to the five‐factor model and its applications. Journal of personality, 60(2), 175-215.
- Paunonen, S. V., & Ashton, M. C. (2001). Big five factors and facets and the prediction of behavior. Journal of personality and social psychology, 81(3), 524.