Less is more - I only take the minimum amount of money, ID, and credit cards on a shore excursion. Passports I always leave in the safe except when required. I take a Xerox copy instead. So far, the only time I needed my real passport was in St Petersburg.
take as little as possible. All you really need is your sign and sail card, your driver's license, a credit card(for any major purchases) a small amount of cash for cab fare and souveniours, disposable underwater camera, sunscreen. Pack in either a backpack or beach tote. Your items are very safe on excursions, and most beaches have lockers for rent.
The same holds if you are doing an excursion, just bring what you need, in most cases you can leave your stuff in a bag on a boat/bus, etc. Always leave the good camera back on the ship and take something that is more durable especially if you are going to a beach. The underwater cameras come in handy for days like that.