Works only in Gecko 20.0 and higher because used API doesn't exist in older versions!

Known issues:

We just inherit private state from selected tab and tries preserve private state of dropped link-like things, this is simple to implement, but may confuse a bit…

Styles:

You can use .tabbrowser-tab[privateTab-isPrivate] (private tab) and #main-window[privateTab-isPrivate] (built-in private window) selectors in styles for userChrome.css/Stylish.
Example styles:

• change underline of private tabs
• change icon
• change background color
• add overlay icon
• add icons to menu items

API for other extensions:

Events:

You can listen for following events:

event.type	event.target	event.detail	Description
PrivateTab:PrivateChanged	tab	1 – private tab 0 – not private	Changed private state of the tab
PrivateTab:OpenInNewTab	tab	1 – may be opened as child tab	Link was opened in new private tab
PrivateTab:OpenNewTab	tab	–	Opened new (empty) private tab

API functions:

boolean privateTab.isTabPrivate(in DOMNode tab)
boolean privateTab.toggleTabPrivate(in DOMNode tab[, in boolean isPrivate])
void privateTab.readyToOpenTab(in boolean isPrivate)
void privateTab.readyToOpenTabs(in boolean isPrivate)

privateTab.isTabPrivate()

Investigates that the tab are private (true) or not (false), example:

// Close all (visible) private tabs:
Array.slice(gBrowser.visibleTabs || gBrowser.tabs).forEach(function(tab) {
	if(privateTab.isTabPrivate(tab))
		gBrowser.removeTab(tab);
});

privateTab.toggleTabPrivate()

Changes tab private state:
Toggle: privateTab.toggleTabPrivate(tab)
Make private: privateTab.toggleTabPrivate(tab, true)
Make not private: privateTab.toggleTabPrivate(tab, false)

// Make all (visible) tabs private:
Array.forEach(
	gBrowser.visibleTabs || gBrowser.tabs,
	function(tab) {
		if(!privateTab.isTabPrivate(tab))
			privateTab.toggleTabPrivate(tab, true);
	}
);

privateTab.readyToOpenTab()

Allows to open private or not private tab (independent of any inheritance mechanism), example:

// Open in private tab:
privateTab.readyToOpenTab(true);
gBrowser.addTab("https://mozilla.org/");

// Open in not private tab:
privateTab.readyToOpenTab(false);
gBrowser.addTab("https://mozilla.org/");

privateTab.readyToOpenTabs()

Allows to open many private or not private tabs (independent of any inheritance mechanism), example:

// Open in private tabs:
privateTab.readyToOpenTabs(true);
gBrowser.addTab("https://mozilla.org/");
gBrowser.addTab("https://addons.mozilla.org/");
// ...
privateTab.stopToOpenTabs();

Backward compatibility:

Check for Private Tab installed (and enabled):

if("privateTab" in window) {
	// Do something with "privateTab" object
}