Great thread. Don't know how I missed it the first time around.
Most recently I brought a cooktop and range hood home from New Zealand. The oven had to go cargo.
I've brought pizzas, sheep in two varieties - an aluminum sculpture and a full-size one from England with real horns and sheepskin and a pinata - maybe that was me you saw

-and inflatable doll, which the entry people at Tortola did manage to find.
The inflatable woman and the pinata were for parties we had when we chartered two sailboats in the Caribbean with 12 friends. We dressed the inflatable woman differently daily and flew her from one of the masts. The pinata got us into a bit of trouble when we decorated one of the boats for our Mexican fiesta night and it began to rain. The crepe paper wasn't color fast and we had red water dripping down all over us and the boat. We scrubbed for hours to get it clean.