Reorder/rearrange tabs using keyboard shortcut
Firefox 19 and later now support these shortcuts natively:
Firefox 19 added shortcuts to move tabs:
- Ctrl+Shift+PgUp to move left, and
- Ctrl+Shift+PgDn to move right.
The change is recorded as bug #364845; here is the specific commit that added the shortcuts.
Therefore, the Move Tabs extension is no longer required; in fact, if you have it installed you should disable it (or else the shortcut will move the tab twice).
For moving tabs to a new window, the Tab Mix Plus extension provides the shortcut Ctrl+Alt+N (this can be customized in the extension's options). For moving the tab into a different window, there's no default shortcut, but you can set it up by changing the merge behavior (Tab Mix Plus Options > Events > Tab Merging) to merge only the current and last-focused windows, and then setting a shortcut for Merge (the default shortcut Ctrl-Shift-M conflicts with a built-in one).
The Firefox extension Move Tabs allows you to define a keyboard shortcut to rearrange your tabs. The default shortcut is Ctrl+Shift+Page Down and Ctrl+Shift+Page Up.
As for doing this without an extension, it is possible, but annoying. Mozilla claims that all you have to do is press Ctrl+Left and Ctrl+Right, but the problem is that focus needs to be on the tab bar. Just clicking the tab bar is not enough to bring focus to it. The easiest way to get focus onto the tab bar is to press Ctrl+L to move focus to the address bar, and then press Shift+Tab twice to move focus up to the tab bar. After the focus is on the tab bar, you can press Ctrl+Left and Ctrl+Right to move the tab. If you happen to already be a user of AutoHotkey, you may be able to write a script to automate this process if you really want to avoid installing an extension.