My daughter has been attending various sleepaway camps for several years. She did a college gym camp last year and will return this year. The packing list on the camp's website covered most everything. The only clothes she actually used were leotards, her swimsuit, and pajamas. She also threw out the healthy snacks I sent with her and ate pizza and candy every evening.
I always send a plastic basket or shower caddy for toting toothbrush, comb, shampoo, and soap, even if the bathroom is attached to the dorm room. When the kids are sleeping in sleeping bags in cabins, I send a flannel fitted sheet to keep the sleeping bag from sliding off the plastic mattress (I learned the importance of this after picking a kid up off the floor in the middle of the night while chaperoning a Girl Scout troop camp). If you don't have flannel, even a regular fitted sheet will help. For college dorms, my daughter likes a foam mattress topper because dorm mattresses can be hard. She also likes to bring one of those spray bottles with an attached fan, especially when there is no air conditioning.
We do not send our daughter to camp with electronics even if the camp permits them, on the theory that texting or calling home increases homesickness. She is always too busy with her new friends to use any solo amusements she packs (books, coloring books, etc.), but sometimes group games like Uno, American Girl quiz books, or Mad Libs will get used. And despite the fact that we always provide her with stationery and pre-addressed mailing labels, she stopped writing us letters her second summer of camp. Each year, we end up sending her with less stuff.