Actually Captain Barbossa came back to life at the end of the Curse of the Black Pearl (episode 1). There was another scene that most viewers did not see because it was shown at the end of the credits. In this scene, Barbossa's monkey retrieves his master's cursed coin from the treasure chest. In so doing, the monkey becomes undead, but also he revives Captain Barbossa albeit once again undead.

However at the end of Dead Man's Chest, Captain Barbossa appears to be mortal (he's eating an apple), so somehow the undead curse has been lifted. Either he has somehow returned the coin taken by his monkey to the treasure chest to lift the curse, or Tia Dalma (Rosie Chavez) has lifted the curse.

At least that's what I'm guessing. I have Curse of the Black Pearl somewhere in my house (can't find it). I'm guessing Dead Man's Chest will be on DVD before the 3rd installment is released, so next time, I'm watching POTC 1&2 in succession before watching POTC3.

Obviously Johnny Depp survives - how is anyone's guess.

Still, all in all, it was a great movie.