You'll need to pack for all seasons when visiting Chile, no matter what time of year you're traveling. Outside the cities, especially in the Lake District and Southern Chile, long-sleeve shirts, long pants, socks, sneakers, a hat, a light waterproof jacket, a bathing suit, and insect repellent are all essential. Light colors are best, since mosquitoes avoid them. If you're visiting Patagonia or the Andes, bring a jacket and sweater or a fleece pullover. A high-factor sunscreen is essential at all times, especially in the far south where the ozone layer is much depleted.
Other useful items include a screw-top water bottle that you can fill with purified water, a money pouch, a travel flashlight and extra batteries, a medical kit, binoculars, and a pocket calculator to help with currency conversions. A sarong or light cotton blanket can have many uses: beach towel, picnic blanket, and cushion for hard seats, among other things. You can never have too many large resealable plastic bags, which are ideal for storing film, protecting things from rain and damp, and quarantining stinky socks.
Since it's sometimes hard to get a bottle of shampoo through customs these days, an easy workaround (and load-lightener) is to buy a handful of shampoo packets (about the size of a ketchup packet) in any Chilean drug store or street market. Of course, many better hotels will already provide shampoo and soap. Though Chile's bathrooms are generally well stocked with toilet paper, it's still not a bad idea to have a small packet of tissues in your pocket.