I always find myself away from home or the hotel for hours on end and even for the whole day when I am in Greece. Visits to museums, to archaeological sites, or the beach can occupy the better part of a day, so I always cary a Back Pack with all the essential items I anticipate needing for the day. In it I always pack my cameras, lots of extra film, a raincoat (which I use for padding at the bottom), a bottle of water, and all the other small items I usually need (pens, lens cleaners, a notepad, extra batteries). It pays dividends to invest in a quality backpack since you will be using it constantly.
Once in Greece during the summer chances are good that you will find yourself in a small boat for a period of time. This is a great experience, except when the waves splash over the speeding boat and land on our expensive photo equipment. It has happened to me and many others as I know, and now I always pack a handful of large Ziploc bags for such cases. Last summer I was riding my mountain bike and a freak rainstorm dropped a ton of water on top of me while I was miles from any shelter. The storm lasted only twenty minutes but dropped enough water to destroy my camera which was likely sheltered in my waterproof waist pouch. A Ziploc bag should be sufficient for such situations and they might be hard to find in a Greek SuperMarket, so pack some before you go.
Pack lots of sun block lotion since it can be a major expense for anyone spending some time at the beach. Sunscreen in Greece during the summer is in high demand, and the prices reflect that. It cost you more than 15 Euro for a small bottle of 30 proof sunscreen, and you can go through it in two or three days if you stay at the beach for a long time.