Rain gear: Waterproof jacket, rain pants, and a decent quality poncho. During nest searching, rain gear is best as ponchos tend to be ripped to shreds by vegetation, but ponchos can keep you and your backpack dry during downpours.
Rubber boots: You can find good quality boots in Cusco (cheaper than North America) but size 10 and above are difficult to find. Consider bringing shoe inserts if you have high arches.
Hiking boots: At high elevation (e.g., generally above 1500m), you can use waterproof hiking boots if you prefer them to rubber boots, though you should still have a pair of rubber boots just in case. In lowlands and middle elevations, rubber boots are highly recommended.
Daypack: Sufficient size to carry water, snacks, field equipment for nest searching, head lamp, field notebook, and rain gear.
Head lamp: Absolutely essential. Back-up headlamps are also a good idea.
Sleeping bag and thermarest: Something that will be comfortable to sleep in for many months!
Socks and foot powder: Keeping feet dry and fungus free is critical for your well-being in the field. Anti-fungal creme is never a bad idea either.
Medicine: If you require prescription medication, you should bring enough to last the entire season. Also, if you are severely allergic to Hymenoptera (bees, wasps, ants) you should bring your own EpiPen. Antibiotics and Metronidozol (for Giardia) are prescription based, so assistants must bring their own if they want to have them on hand.
Recipes for cooking: Assistants take turns cooking for the crew at each station, so it is good to have some ideas for meals in your back pocket (and ways of being creative with field food).
Money: Assistants need money for personal things (e.g., shopping while in town, using internet, buying special food and snacks) and also for their one-week travel vacation during the season (fall assistants only). Usually volunteers bring between $400-700 in the field with them for personal items. ATMs in Cusco will accept North American bank cards.