I am trying to change the background color of my tabs in a JTabbedPane. I tried JTabbedPane.setBackgroudAt(0, Color.GRAY) and JTabbedPane.set
You should consider using a Look and Feel that does what you want, or failing that, changing the default UIManger settings for a JTabbedPane:
UIManager.put("TabbedPane.background", Color.GRAY);
If you opt for the latter, it must be done before you create your GUI.
For more on this, please see Rob Camick's excellent blog on the subject: UIManager Defaults.
Edit: I was wrong. It should be:
UIManager.put("TabbedPane.unselectedBackground", Color.GRAY);
But note that this may not work with every Look and Feel.