Firefox 4 introduces App Tab, similar to Pin Tab in Chromium. Its actually Pin tab since you use Pin as App Tab to make a tab as App Tab, and it does look like Pin Tab as in Chromium, the tab handler shrinks down to icon only and the tab is moved to the left-most side after already pinned tabs.

Its easy to write a quick command, so certain websites can be pinned automatically. The following code is for pinning a music website:

" Auto-pin
autocmd PageLoad listen.grooveshark.com js if(!getBrowser().mCurrentTab.pinned) getBrowser().pinTab(getBrowser().mCurrentTab);

I dont think its necessary to check if mCurrentTab is pinned, but thats what I wrote firstly.

You can also write a more general function and match all URLs, so if a page which doesnt need to pin is loaded but the tab is current pinned, you can unpin it using getBrowser().unpinTab().