You're most likely looking at using a flash/silverlight/activeX control. The <input type="file" /> control doesn't handle that.
If you don't mind the user selecting a file as a means to getting its directory, you may be able to bind to that control's change event then strip the filename portion and save the path somewhere--but that's about as good as it gets.
Keep in mind that webpages are designed to interact with servers. Nothing about providing a local directory to a remote server is "typical" (a server can't access it so why ask for it?); however files are a means to selectively passing information.
Eventhough it is an old question, this may help someone.
We can choose multiple files while browsing for a file using "multiple"
<input type="file" name="datafile" size="40" multiple>
Stumbled on this page as well, and then found out this is possible with just javascript (no plugins like ActiveX or Flash), but just in chrome:
https://plus.google.com/+AddyOsmani/posts/Dk5UhZ6zfF3
Basically, they added support for a new attribute on the file input element "webkitdirectory". You can use it like this:
<input type="file" id="ctrl" webkitdirectory directory multiple/>
It allows you to select directories. The multiple attribute is a good fallback for browsers that support multiple file selection but not directory selection.
When you select a directory the files are available through the dom object for the control (document.getElementById('ctrl')), just like they are with the multiple attribute. The browsers adds all files in the selected directory to that list recursively.
You can already add the directory attribute as well in case this gets standardized at some point (couldn't find any info regarding that)
Source: Stackoverflow.com