The IPIP-NEO personality test (International Personality Item Pool Representation of the NEO PI-R) looks at 5 broad domains and 30 sub domains of personality. While the full IPIP test consists of 1,699 items, the link leads to a short test of 120 items.
The IPIP-NEO is more complex than the more popular Myers Briggs personality type and as such gives a more indepth look of the personality of an individual, including those aspects that would be considered negative. One weakness I would give this test is that it is a self-assessment, so honesty with yourself is important.
I thought the results of my own test were pretty accurate; the only part that I thought was inaccurate were some of the scores under Neuroticism that I thought should have been higher (more negative). That could just be a lower view of myself than is accurate, though.