As already pointed out, Agile does not mean little to no documentation - "working software over comprehensive documentation".
The way I approach documentation is almost to flip things on its head and to consider just about everything part of documentation (including code and unit tests as technical specs). So, a story (or whatever other mechanism you use to divvy up work) describing a business/user requirement should be detailed enough to be estimated by the team doing the work; otherwise, it is incomplete and vague. Further, something I do in my own practice, if the story (or whatever) is estimated to take longer than one working day to fit the team's definition of "done" it should most likely be broken down (this atomizing then compiling eventually leads to pretty extensive documentation, but does not assume as many unknowns as not doing it will - and can lead pretty interesting reuse and pattern revelations).
Example using BDD style requirements:
Given I am working on a document
When I select "Save As..."
Then a menu should appear allowing me to choose a name,
and a file type,
and a location in the file system,
and a file should be created in the file system
We may need/want to add UI elements to accomplish this, menu items, storyboards, keyboard shortcuts, etc. to this description (we may have multiple variations on the same theme of "saving a file"). And so on.
All of these related artifacts can be attached onto the base story/requirement; resulting in more complete documentation. But, only add those stories you actually implement to your documentation of the web version of the software.
Here's where things get kind of flipped on their head and become more "Agile". During development, and after development, revisiting the documented requirement and adding changes/modifications/improvements made by the team edits are made (without having to go through a documentation-only CCB). The ability to edit/update the documentation and related assets without going through all the review boards and whatnot - or throwing the document "back over the wall" when we find out during development that the document is incomplete in some way makes us able to adapt to the unknowns - therefore, Agile.
This documentation should have some form of version control or history, which allows us to describe the system we desired, but also describe the system that was actually implemented - noting another answer/suggestions regarding documentation being part of the Definition of Done (something I also do). (Wikis are good for this; however, a fully integrated concept is a little more desirable - e.g., being able to relate a ticket to a file in trunk in the version control system would be nice.)
To kind of conclude. Creating exhaustive documentation up front, which cannot be altered during and/or shortly after the development effort, will keep you from being agile - able to quickly adapt to unknowns. However, to reference Leading Lean Software Development, wherein they mention that if policies do not allow for certain practices/processes to be used properly, then it doesn't matter if you say you are lean (or scrum, or agile).
One way to make sure you are not being overly exhaustive - probably could've used this mindset on this answer - is to only write what you need to when you need to (similar concepts exist in development in general). Another would be to get everyone to understand that you don't need to try and figure everything out up front (the biggest transition from Waterfall to Agile) - we will document every idea and it may or may not end up in a release. And, finally, deprecate (and remove) anything that no longer applies...I remember seeing documentation for a system once and, when I reviewed the system, half the document didn't actually apply to the system anymore.
