This is a generic list, to help you brainstorm for an outing. Please consult your troop leaders about any special needs for the specific trip you are attending.
Scout uniform (Girl Scout vest or sash, or Boy Scout shirt, hat, T-shirt, etc.)
Several changes of layered clothing (t-shirts, shorts, pants)
Undies and socks
Pajamas (or sweatpants and a t-shirt to sleep in)
Jacket (for cold evenings) - polar fleece is best because it is still warm if it gets wet
Sneakers/hiking boots/sensible walking shoes (Waterproof hiking boots are good for walking through wet grass or mud.)
Flashlight (for walking at night and reading at bedtime) or lantern
Rain gear (an inexpensive poncho works well and will fit for several years as children grow)
Bandana or hat
Swimsuit, pool towel, swim goggles (if swimming is available)
Sunscreen, bug repellant
Bag for dirty laundry, plastic bag for wet clothes
Grooming supplies (toothbrush, toothpaste, deodorant, shampoo, soap, washcloth, comb)
Shower shoes (like cheap flip-flops)
Towel for showering and face washing, washcloth if desired
Sleeping bag, pillow. Sheet for covering the mattress, if needed. Foam or air mattress if mattress is not provided.
Something to do in case it rains (deck of cards, sketchbook & colored pencils, origami paper, etc.)
A book to read in bed during quiet time before lights out (or an activity book - seek-a-word, etc. - and a pencil), plus a book light or flashlight.
Non-refrigerated snacks (applesauce cups, nuts, raisins, dried fruit, trail mix, granola bars, etc.) (if they are allowed)
Refillable water bottle, plus something to carry water bottle in on hikes (lightweight bag or bottle strap, such as this carabineer one or this cheap one from Oriental Trading to buy, or, if you want to make one, this great kids-can-make-it one or this o-ring one or you could crochet this one.)
Mess kit, silverware, mesh bag. (Target carries inexpensive mess kits - about $5. Nicer stainless steel ones are available at Dicks Sporting Goods. A mesh lingerie bag to hold dishes for drying runs about $2.50 at PathMark. Sturdy plasticware utensils will do, or odd silverwear you don't mind losing.)
Small pack of tissues, toilet paper
Swiss Army knife (if it is allowed)
Medications (anything you take regularly, asthma inhaler, Benadryl, calamine lotion, Tylenol)
Small first aid kit (band-aids, moleskin for blisters, etc.)
Spending money, if needed (wallet)
Cell phone and charger.
Backpack or duffel bag to carry and stow your gear. Lightweight backpack for carrying things as you walk around camp or go on hikes.
Younger girls may want to bring one small, sturdy, stuffed animal or other comfort toy. (Choose one that can be lost without causing major distress. )
Girl Scouts usually need a Sit-upon (and possibly lightweight backpack or bag to carry it).
Directions to the campground, if you are driving.
NOTE: Shower before you leave home, as shower facilities and time may be limited.