IQ is measuring something real and important to life outcomes (the so-called g factor) but it is not everything that matters to life outcomes or cognition. As Keith Stanovich pointed out in What Intelligence Tests Miss, IQ is not the same thing as rationality. Your intelligence can defeat itself if misapplied. And due to human nature, it will. The more clever you are, the more ways you can deceive yourself. Reading the Sequences (or RAZ) can help you learn to stop doing that.
Why wouldn't you want to know your own IQ? Are you afraid a "bad" result would become a self-fulfilling prophecy? If you want to be more rational, then the truth is not something to be afraid of! You have been living your whole life with whatever IQ you have. Knowing your own strengths and weaknesses doesn't change what they are. It just gets rid of the weakness of not knowing that.
There are multiple components to IQ tests. You may be stronger in some areas than others. In my case, the IQ test revealed that I have a learning disability, despite having the overall genius IQ typical of LessWrong readers (or at least LessWrong survey takers).
Learning about this was not a disappointment. It was a relief. I had always felt like I somehow wasn't measuring up to my own apparent potential, but now I realize it wasn't my fault. Now that I know what my weakness is, I can better compensate for it, and better leverage what strengths I have.
While we don't know good ways to improve fluid intelligence by much (besides avoiding those things that make it worse, like sleep deprivation, etc.) there are well-known ways of increasing your crystallized intelligence: Read more and better books. Listen to audiobooks during your commute. Use SRS and mnemonics. Specialize. You can generally out-learn someone a bit smarter than you if you develop better study habits. And you can expect to far out-learn someone who isn't even studying your field.
You can also increase your effective fluid intelligence in many useful situations by using external tools. Working memory is consistently one of the worst bottlenecks in human cognition. Write things down when thinking. Draw diagrams. Take pictures.
Learn to use a computer more effectively. Try org-mode or FreeMind or TiddlyWiki. Learn to use a spreadsheet. Try AutoHotKey to improve your efficiency. Learn Python, if you can. Try working through a math book with Mathematica instead of pencil-and-paper. There's a night-and-day difference in effectiveness between an illiterate genius and a merely bright person who has access to a PC and Google and knows how to use them.
I agree with both Dagon and TheWakalix. Generally speaking, more knowledge is better; with the exception of misleading incomplete knowledge, which can be overcome by more and better knowledge. And "knowing thyself" is especially important. Therefore I would definitely want to know my IQ, and also know exactly what it means and what it doesn't mean.
Why? If you took a test, and it came back telling you that you had an IQ of 140, what about your day-to-day life would change? Likewise, what would you do different if you took a test and it came back telling you that you had an IQ of 90?
I think it would pretty significantly influence which career paths I would choose. If it came back with an IQ of 90 I would be very hesitant to go into mathematics, or really research professions in general, since those tend to be both pretty heavy-tailed and seem to rely on having a high general intelligence. I would be much more likely to choose a profession that is more standardized and has less variable outcomes (most service industry jobs seem to fit reasonably well here).
Also lots of other things, like how much I should trust my own judgement vs. relying on tradition and well-established norms. It's not like this single piece of information would totally dominate my considerations, but it would add up to a general self-model that might include realizing that I am likely to be wrong when challenging tradition and established rules, and having a higher IQ should make me at least a bit bolder in challenging existing rules, since I would be more likely to actually get it right.
Also simple other things, like how much effort to put into getting high SAT scores, which would determine lots of college admissions (or whatever my local country's equivalent of the SAT is). I would be more hesitant to switch professions, since I would expect to be less good at learning new skills than other people.
(Note: Thrasymachus's response gets the basics right, in that I would expect most people to have a pretty good guess of their broad competence already. Knowing your IQ score is unlikely to be the most critical piece of evidence you will get on that, but if it's really out of line with all the other evidence you have about yourself, then I would pay attention to that and try to figure out what's up.)
If an IQ test came back significantly higher than I expect, then I'd start to think I'm underperforming my potential, and I'd look for reasons for that. Perhaps there are skills missed by the test that I'm unusually weak on, like maybe I give up quicker than average if I find something hard. Then I can work on those skills, or position myself to avoid relying on them.
Conversely, if it came back lower than I expect, I'd think that perhaps I'm unusually strong in those skills, and I'd be able to position myself to take advantage of them.
If an IQ test told me that I have an IQ of 90... and if I would have a good reason to believe the test's reliability... I would be extremely confused.
An IQ test giving me a result of 140 or higher, really wouldn't do anything useful, but that's because I already know. (Telling you an information you already know is useless. That doesn't mean the information was useless in the first place; just that its another repetition is.)
For me, knowing of my high IQ provided partial explanation to things I perceived in my life. (It was not a full story of course; one needs to also take into account high neuroticism, and probably some undiagnosed autism. But again; knowing about these concepts further improved my self-understanding.) Such as "why are most people so uninterested in things that I find fascinating?" or "why is learning at school so easy to me, except for subjects that are mostly memorization?". Or "where could I find people similar to me?".
There were alternative explanations, such as "the topics I am interested in are inherently weird" or "learning is easy to me because I spend a lot of time reading stuff", which seemed to almost fit, but not completely. (For example "because I read stuff" is yet another thing that needs to be explained; why I like reading about things, but most kids don't?)
On SSC, someone claimed it helped show that lead poisoning was a problem.
Those studies aren't done on an individual level. It has little to do with the usefulness to know your own IQ.