Firefox is one of the more cagey browsers about web storage, as I can`t see any built-in mechanism for allowing users to see what data is stored in local storage.
Now roaming around on the web, there are various suggestions as to how it can be done, such as downloading some kind of SQLite Manager or Firebug.
However these are really web developer tools, and way beyond what most users want, just to see if there is any data stored in local storage.
Eventually I found a Firefox extension called Foundstone - it is available from the Mozilla website, it is simple to install, and works well.
Once it is installed, it appears in the Tools drop down menu as "HTML 5 Local Storage Explorer", and it provides a simple view of what data is installed in local storage.
You can delete all the data, or double click on one line and see it in a bit more detail.
-------------------------------
Judging by various comments on some forums, Firefox is a bit iffy about actually allowing websites to use web storage, even if it is set up to allow it.
I sort of confirmed this, as in order to take the screenshot above, I found it quite difficult to persuade Firefox 16 to save any data in local storage.
Users can configure Firefox using "Edit / Preferences / Privacy" so that web storage is not allowed - or at least - it doesn`t work.
Private browsing mode sets a number of parameters to provide private browsing, but they may not include the barring of web storage - Mozilla has got itself in a bit of a twist over privacy - if you look through the Mozilla website you find conflicting information about when or if local storage is allowed or denied.
There also seems to be variation depending on which version of Firefox you are using.
My preference is to ignore "Private browsing mode", and instead tick the bottom box to "Clear history when Firefox closes", then click on settings, and tick every box.
-------------------------------
If you want to be a bit more confident that Firefox will not allow local storage, then you can dig into the "about:config" configuration page, and change two of the settings -
dom.storage.default.quota ....... 5120 dom.storage.enabled ......... true
Change these to
dom.storage.default.quota ....... 0 dom.storage.enabled ......... false
-------------------------------
In Firefox, local storage is stored in a file in your profile - it probably depends on what operating system you are using, but you might find it in a location such as "<username>/.mozilla/firefox/???????.default/webappstore.sqlite".
As for Opera, I think that these settings only apply to local storage, I haven`t found any settings that control session storage, so it should be assumed that websites can continue to use session storage.
Session storage should of course be deleted when Firefox is closed, but you may want to be certain by killing any data that is stored in volatile storage by shutting down the computer, and switch it off at the wall for several minutes.
Doing a restart or sleep mode may not delete data in volatile storage.
-------------------------------
I do wonder about where Firefox is going to end up - there is some comment on the web that Mozilla doesn`t like the concept of web storage, and as much as it can it is making it difficult for web developers to use it.
However they are getting pushed into things - possibly by Google - Mozilla receives a lot of funding from Google, so Google can call the shots - and Google uses web storage.
The other thing that Mozilla have done is to remove the ability to disable JavaScript from the Preferences menu.
On the most recent versions, you have to go into "about:config" and do it from there.
Web storage of course requires JavaScript, and so does Google Analytics, so Google would be very keen for Mozilla to stop people disabling JavaScript.
Sad !