’Create application shortcut...' Chrome's feature in Firefox?

New Update 2020

Please see Amer's excellent answer. (If you want the icon to remain in the taskbar, right-click it and click "Pin to taskbar".)

Caveats:

• Since the Site-Specific Browser (SSB) feature is disabled (off) by default, it might be experimental.
• There's no "Loading" progress indicator in the SSB window. Sometimes you'd stare at a blank window and wonder what's happening.
• There's no Zoom function. If you had already set Zoom level in Firefox main window, it doesn't carry to the SSB window. It's always at 100% zoom level.
• The window title never changes. It's always the fixed title. This is bad for web-apps that change the title to indicate something. (I suppose the icon may not change either.)
• If you had already enabled notifications via Firefox main window you may get them, however if you've never enabled it, I'm not sure if you can enable it from the SSB window.
• There's no standard right-click context menu - not even on text fields. This really hampers usability since you cannot copy, paste, refresh page, etc. without using keyboard shortcuts. (Application-specific right-click menus still work, since these are part of the website's own code, not from the browser itself.)
• The web app's window doesn't remember its last position and size.

These caveats make the SSB solution less than ideal right now. Hopefully they fix these in future FF versions. But if all you're looking for is a dedicated window for your web-app through Firefox, it's a good solution.

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Previous Update 2017

You can sort-of do this now, with a small config change and a bookmarklet. (I have not experimented with desktop shortcuts, but it might be possible.)

1. Go to about:config and set dom.disable_window_open_feature.location to false.
   This is optional, but it removes the disabled location bar at the top of the window.

2. Create a bookmarklet (that's really just a regular bookmark but executes Javascript):

    javascript:(function(){window.open("https://www.google.com/","_blank","menubar=no,location=no,toolbar=no,scrollbars=yes,left=150,top=50");})();
   

   Replace https://www.google.com/ with your URL.

When you open this bookmarklet, it will open the site in a separate dedicated window. You may want to adjust the values of left and top as needed.

Bonus Tip: If you have "Show your windows and tabs from last time" enabled, when you exit and restart Firefox with the dedicated window open, it is also restored.

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Previous Answer

Update: Support for this flag appears to have been removed from the latest versions of Firefox.

Firefox has a terribly under-documented flag -chrome:

firefox.exe -chrome http://superuser.com 

Like Chrome application shortcut:

• Creates a basic window with just the web page and the plain window chrome (no tab bar, address bar, etc).
• Usable as an "application".

Unlike Chrome application shortcut:

• The window is always created with the full size of the page. For AJAX-based empty pages that only fill themselves after page-load, this would result in a very tiny window at the top-left corner of the screen. Thankfully you can manually resize the window.
  • If you try superuser.com, you will get a window that's very very long.
  • Undocumented flags -width and -height do not work.
  • It may be possible to have a post-launch process find the window and adjust the window size automatically, but that seems too much work for the average user.
• Favicon is not used as the window icon. The window still has the Firefox icon.
• In Windows taskbar grouping, the window is grouped with Firefox's main window. In Google Chrome, an application shortcut really runs as separate Windows program and is not grouped with Chrome's main window.
  • Due to this, if a shortcut to the app is pinned in the taskbar, the shortcut doesn't become the window of the app.
  • Also, exiting Firefox will close the app. Launching again will not restore the app even if Firefox is set to restore all tabs and windows.
• No right-click menu. No back-forward functionality (even with keyboard shorcuts). Cannot reload or zoom. Doesn't remember zoom set in Firefox main window.
• Using arrow keys to move text caret when typing in a textbox can sometimes produce weird results.
• This feature sometimes causes Windows to enter a black screen and come back with "Windows Basic Color Scheme" mode (all Aero effects will be gone). I would classify this as a bug. It doesn't always happen.
  • If this happens, open command prompt and run net stop uxsms followed by net start uxsms.

Other than the above problems, it works fine.

Mozilla Prism (formerly WebRunner) by Mozilla Labs featured the "Create application shortcut" in Firefox:

Mozilla Prism (formerly WebRunner) is a product which integrates web applications with the desktop, allowing web applications to be launched from the desktop and configured independently of the default web browser.

Users can manually create web applications using Tools > Convert Website to Application.

However, since November 2010, Prism is listed as an inactive project at the Mozilla labs website. On February 1, 2011, Mozilla labs announced it would no longer maintain Prism.

There were several alternatives to Prism, but it seems that all of them have been discontinued and are no longer active or available for download.

In the following question: Why is Firefox Prism not in the repositories anymore?, there are two useful answers, regarding the discontinue of Prism and possible alternatives and solutions. It was mentioned that web application support in Firefox is currently in progress. Also, some workarounds have been suggested.

New Update 2020:

With FF (Firefox) you can now natively get the same experience as Google Chrome without the need for a JavaScript shortcut:

1. Update to the latest version of FF.
2. Open "about:config" setting page.
3. Search for "browser.ssb.enabled" Boolean and set it to TRUE (or create a new Boolean with that name if not exist).

4. Restart FF.
5. Open your favorite website in FF, then click on the … (3 dots button) beside the address bar to open the Page Action menu and select “Use this site in App mode”.
6. A shortcut will be placed on your desktop and the app will open immediately.