Are Rorschach tests still used as a diagnostic tool today, or are they just a relic from the 60's? If they are still in use, what sort of information do they provide?
Yes, they are still in use, and they provide rather bad information. My former advisor once worked with a clinician who told him that the main reason they're any better than using the weather report as a projective stimulus is that the Rorschach tests have been in use as-is for decades. Hence we have a better understanding of how people normally react to them, and some catalog of unusual reactions that have been associated with particular characteristics. Had we started with a set of weather reports and stuck with them though, maybe not much else would be different.
Anyway, here are some excerpts from Wikipedia about usage:
The Rorschach test is used almost exclusively by psychologists. In a survey done in the year 2000, 20% of correctional psychologists used the Rorschach while 80% used the MMPI. Forensic psychologists use the Rorschach 36% of the time. In custody cases, 23% of psychologists use the Rorschach to examine a child. Another survey found that 124 out of 161 (77%) of clinical psychologists engaging in assessment services utilize the Rorschach, and 80% of psychology graduate programs teach its use. Another study found that its use by clinical psychologists was only 43%, while it was used less than 24% of the time by school psychologists.
Many psychologists in the United Kingdom do not trust its efficacy and it is rarely used. Although skeptical about its scientific validity, some psychologists use it in therapy and coaching "as a way of encouraging self-reflection and starting a conversation about the person's internal world." It is still used, however, by such prestigious mental health organisations as the Tavistock Clinic.
Shortly after publication of Rorschach's book, a copy found its way to Japan where it was discovered by one of the country's leading psychiatrists in a second-hand book store. He was so impressed that he started a craze for the test that has never diminished. The Japanese Rorschach Society is by far the largest in the world and the test is "routinely put to a wide range of purposes". The test has recently been described as "more popular than ever" in Japan.
The general goal of the test is to provide data about cognition and personality variables such as motivations, response tendencies, cognitive operations, affectivity, and personal/interpersonal perceptions. The underlying assumption is that an individual will class external stimuli based on person-specific perceptual sets, and including needs, base motives, conflicts, and that this clustering process is representative of the process used in real-life situations. Methods of interpretation differ. Rorschach scoring systems have been described as a system of pegs on which to hang one's knowledge of personality. The most widely used method in the United States is based on the work of Exner.
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The whole controversy over the Rorschach test leads us to see it as a useful medium but not as a valid personality test.
In using the Rorschach test, the tester should then focus on how the subject considers the test procedure, the pictures and how he/she identifies the inkblots... or refuses to, rather than focus on what the subject tells he sees.
As @NickStauner states, in this regard you could even use weather forecasts as a test medium... Rorschach inkblots in this respect are probably appreciated because they show a rich palette of patterns and colors which have already been listed and commented.
I highly recommend the book What's Wrong With The Rorschach by Lilienfeld et al which explains the psychological reasons why clinicians use the test and believe it works even though there is no evidence at all for its validity except for highly bizarre responses correlating with thought disorders and food responses correlating with dependence needs. This book is one of the most interesting books in psychology full stop for students and lay readers as it examines the culture, delusions of power, biases, resistances to science, and more that have affected far more psychologists than they should have given clinical psychology was supposed to be a science. Those problems are what led to science-minded psychologists breaking away from APA to form the legitimate science body of psychology in the United States, the Association of Psychological Science. The science of evaluation finds validity of conclusions is increased the more you can integrate: history, observations, collateral tests or interview, and personality tests (however the latter can be invalidated if the patient is unmotivated or lies in answering paper and pencil tests). The Rorschach however adds no validity, and has the potential to reduce it.