I buy the following when I go to chinese supermarket;
Frozen: takoyaki (octopus balls), eel in sauce, dim sum for steaming at home, gyoza.
Dried; glutinous rice flour (for making mochi or leen go), huge containers of cornflour, desicated coconut, panko, dried mushrooms, red beans for sweet soup or paste (filling for mochi), various seaweeds for making stock, in salads, sprinkling on stuff.
I really like smoked tuna stuff so I get smoked tuna fish stock and the katsuobushi shaved tuna flakes.
Soba noodles, vacuum packed udon noodles, Nissen noodles in black garlic flavour or sesame.
Snacks; tempura crisps things, mami monster noodles, pocky, peanut mochi, dried shrimp floss, whole dried fish with chilli (they make your breath stink though...)
Also mirin, sake, dark soy, light soy, rice vinegar, choya plum wine, genmaicha brown rice tea (it tastes like popcorn).
If they have kabocha pumpkin (wrong time of year but for future reference) they are the best pumpkins, so tasty!
Chinese pears are very refreshing, pomelo, daikon radish. Cream cakes that look like Swiss rolls.