For me, it depends on what I am planning to do the rest of the day and whether I've brought my full scuba equipment or am renting.  I think the essentials in a dry bag are IDs and PADI cards, log book, money or credit cards, towel, shorts and a t-shirt, sunglasses, and sunscreen.  I also try to consider the size boat I am on.  If I am on a small boat where you can't even really walk around, I try to be respectful and not bring anything more than I will use on the dive.  Hopefully, if you are on a boat like that, the shop has a secure place you can leave your dry bag for when you return from the dive.  Even on a large dive boat, I try to bring the smallest dive bag possible, especially when I have all my own dive equipment so I am not a space hog.