Here's a site which has a good selection of free personality questionnaires:
I find that questionnaires of this type rarely give any novel information that you wouldn't know about yourself already, and be able to describe in a short self-descriptive paragraph. Many such questionnaires are actually copyrighted, and one needs to pay a fee just to have a copy. I've always had a bit of a problem with this, as I think it exaggerates the importance of what is usually a simple set of questions, which in my opinion should usually be in the public domain. It is annoying to read a journal article about questionnaires (which are often referred to, in a somewhat aggrandizing way, as "instruments," as though we are talking about some kind of highly sophisticated engineering technology), where the copyrighted questionnaire is referred to in the article, but you can't actually see the questions!
But spending some time with these things can have a few positives:
1) a framework for reflection -- sometimes questionnaires can deal with questions or phenomena which are relevant, but rarely thought about or discussed. The questions can be a cue or a framework to contemplate issues. Some of these issues could be addressed in a therapeutic discussion.
2) entertainment -- it can be an interesting or possibly enjoyable activity to fill out questionnaires, and compare your results with others in the population.
It would be important to resist any tendency to be self-critical about your results; everyone will have a unique set of responses, some of which may change over time, or be mood-dependent, as well. Questionnaires are an imperfect way to measure any sort of characteristic anyway. But in any case, a questionnaire is a bit like a lens or a camera--it produces data which can be informative. Sometimes the information can be unique or interesting, like a clever snapshot of yourself from a camera; but other times the information may not be very unique or interesting at all (like a poorly-lit or blurry snapshot of yourself). Even if you may have issues with the way a particular questionnaire is constructed, it can be interesting to see how your responses compare on a percentile basis with others. You may find certain phenomena about yourself that you previously thought were quite extreme, are in fact really quite close to the population average. Or you might discover there are other phenomena which are farther from the mean. Any of these findings might be a subject of future therapeutic dialog.