NOTE: I had tons of problems until I disabled Tree Style Tab, and the plugin does warn to disable other extensions that manipulate tabs.

I've tried more than a dozen tab extensions over more than a decade. This is the best by far. It's rock solid and includes automatic backups that you can browse through and restore. You can have anything from a simple list to a compex structure of panels, each containing tabs and groups of tabs nested together as deep as you like. The customization options are insane without ever leaving the GUI.