I know this is holy war territory, so please read the question to the end before answering.
There are many cases where written specifications make a lot of sense. For example, if you're a contractor and you want to get paid, you need written specs. If you're working in a team with 20 persons, you need written specs. If you're writing a programming language compiler or interpreter (and it's not perl), you'll usually write a formal specification. I don't doubt that there are many more cases where written specifications are a really good idea. I just think that there are cases where there's so little benefit in written specs, that it doesn't outweigh the costs of writing and maintaining them.
EDIT: The close votes say that "it is difficult to say what is asked here", so let me clarify: The usefulness of written, detailed specifications is often claimed like a dogma. (If you want examples, look at the comments.) But I don't see the use of them for the kind of development I'm doing. So what is asked here is: How would written specifications help me?
Background information: I work for a small company that's developing vertical market software. If our product is easier to use and has better performance than the competition, it sells. If it's harder to use, even if it behaves 100% as the specification says, it doesn't sell. So there are no "external forces" for having written specs. The advantage would have to be somewhere in the development process.
Now, I can see how frozen specifications would make a developer's life easier. But we'll never have frozen specs. If we see in the middle of development that feature X is not intuitive to use the way it's specified, then we can only choose between changing the specification or developing a product that won't sell.
You'll probably ask by now: How do you know when you're done? Well, we're continually improving our product. The competition does the same. So (hopefully) we're never done. We keep improving the software, and when we reach a point when the benefits of the improvements we've added since the last release outweigh the costs of an update, we create a new release that is then tested, localized, documented and deployed. This also means that there's rarely any schedule pressure. Nobody has to do overtime to make a deadline. If the feature isn't done by the time we want to release the next version, it'll simply go into the next version.
The next question might be: How do your developers know what they're supposed to implement? The answer is: They have a lot of domain knowledge. They know the customers business well enough, so a high-level description of the feature (or even just the problem that the customer needs solved) is enough to implement it. If it's not clear, the developer creates a few fake screens to get feedback from marketing/management or customers, but this is nowhere near the level of detail of actual specifications. This might be inefficient for larger teams, but for a small team with low turnover it works quite well. It has the additional benefit that the developer in question often comes up with a better solution than the person writing the specs might have.
This question is already getting very long, but let me address one last point: Testing. Like I said in the beginning, if our software behaves 100% like the spec says, it still can be crap. In fact, if it's so unintuitive that you need a spec to know how to test it, it probably is crap. It makes sense to have fixed, written tests for some core functionality and for regression bugs, but again, this is nowhere near a full written spec of how the software should behave when. The main test is: hand the software to a user who doesn't know it yet and tell him to use the new feature X. If she can figure out how to use it and it works, it works.