It really depends on the ages of the group. We have young kids so I have to carry a backpack with a set of clothing for my youngest in a ziplock bag). If I didn't need to I would bring only water, as large a towel as I could fit in my waist bag, sunblock (you need to reapply several times a day) my camera (in a zip lock bag in case of rain), a few Tylonol, and money. I also bring extra pony tail bands because my daughter and I have long hair. Because I carry a back pack I carry ponchos, spare socks (if your socks get wet you may get blisters) and Gold Bond powder (which is great for feet soothing, and anti chaffing. I also bring trail mix or nuts to snack on and sometimes apples or oranges. Some people carry band aids, chapstick, a brush or comb...
Sunblock and a towel are my must haves. The towel has hundreds of uses. You can dry a bench seat or ride seat or bus seat before you sit down, sit on it for parades, use it as a small blanket in air conditioning, use it to flag down your husband in a crowd (wave it to get his attention), and we used it to hold space for parade/firework viewing (it is very hard to hold 'empty' space, but put a towel down and everyone knows you mean to reserve the spot). I most often brought a few towels because I had the back pack and it was the only thing we really missed if we forgot. We would just use the towels from our room and switch them out for clean ones each day.
If there is anything you find you need and don't have with you in the parks just ask. They have loads of stuff they do not display.