I get this question on occasion, when friends go overseas. And I'm usually stumped. Then a few days later, or even weeks later, I'll think of something. Or I'll mention it to someone and they'd say, 'Did you ask them to buy ...?'
So for convenient reference, here's a list of eternally useful items I'd always be grateful for and am always on the lookout for myself.
Scarves. It somehow became a habit to always have one in my bag, since I usually leave the house under the scorching midday sun for a freezer of a workplace. No one can escape the buses and the cinemas either. So brightly hued cotton/silk accepted. Wool and neon colours excepted.
Toiletries. Lotions, shower foams, shampoos, toothpaste, in sizes that meet customs regulations - 100ml or under. I hoard these for my travels. Unfortunately, liquids weigh down luggage. On the bright side, local products always come with their own unique fragrances.
"Art". A lacquered Tin Tin picture worked in Cambodia, handcrafted earrings in Australia, a cotton-woven picture of a topless woman in India, a paper lamp of flower pressings in Thailand, handmade recycled paper in Africa ...
Food. From the bee farm, the fish farm, the milk dairy, the fruit orchard, the salt fields, the tea plantation ... and the Japanese supermarket!!!