I'm a little surprised no one has mentioned Escape Rope.
I always make sure I have a couple of those. Think about it, you're in a cave, 5 of your Pokemon are fainted and you ran out of revives. Your sixth Pokemon is weak, but you hold onto it because you want it to gain some levels. You're too far away from the exit and you don't want to faint in battle, or have to pay a trainer your money. So you use an Escape Rope to get out of the cave to heal your Pokemon immediately.
Items I like to hold onto: Repels, Escape Rope, Pokeballs, Ultra Balls (in case of a Legendary encounter), Revives for long journeys, items that can cure HP and PP and status. I always try to save the Elixers and Ethers for the Elite Four. Amulet Coin is a good item to use when battling the Elite Four. Also, I like items that power up type moves. For example, Charcoal for fire pokemon, mystic water for water Pokemon, and miracle leaf for Grass Pokemon.