Peru being the hiking and trekking mecca that it is, there are a ton of camping opportunities.  In general, travelers will not be responsible for their own equipment (tent, sleeping bag, camping stove etc) as most camping trips are organized through tour operators who provide (or rent) all types of gear.  However, if you are planning on doing a lot of camping it's not a terrible idea to bring some of your favorite (or most personal) items.  In the Huaraz and Cusco regions the number of options for trekking or climbing in combination with camping is almost unlimited.  Camping is commonly combined with other multi-day outdoor activities such as biking or whitewater rafting.
The majority of the camping is done in the Cusco region—where the combination of the jam-packed Inca Trail and the accompanying Sacred Valley provide visitors with a multitude of camping possibilities.  Most treks in the region can be organized through guiding companies in Cusco.
Huaraz, Peru's climbing capital, predictably has lots of camping.  However, the camping is merely a necessary element of summiting one of the several nearby peaks.  For those not going up the mountains, there are also camping and trekking options throughout the Cordillera Blanca. 
Peru's multi-day white-water rafting trips include camping as well.  Most of them leave from Cusco (although you will put-in the river hours from the city).  The outfitter will provide all necessary equipment. 
Along the coast and in the mountains there are camping options as alternative to hotels.  If you plan on this style of camping you will want to make sure you place your tent in a safe place and that (ideally) the campground has a place to lock up valuables.  People have been known to camp on the beach in Peru, but ask around before to make sure it's safe.