Almost anything can be considered an "omiyage" (souvenir/gift), here's just a little of my favorites...
Potato products (jagapokkuru)
Dairy products (cheese, butter, ice cream)
Umeda & Osaka
*anpan (buns with sweet beans) from Kokoroniamaianpanya --I often bring these to my MIL.
*nama choco daifuku from Korakudo --It's seasonal, usually around winter-time.
*Tommy's An Bread
*Ca Marche's patchwork bread
*Le Dimanche pastries
*La Pierre Blanche sweets
*shibazuke (tsukemono with shiso (perilla)) from Doi Shibazuke tsukemono : in some department stores around Japan : info in Japanese
*chirimen tsukudani from Shinonome
*tsukemono (pickled veggies) from Uchida Tsukemono tsukemono (shop in Nishiki-market): info in Japanese
*Bigot (info in Japanese)
*Doughnuts from Donuts Dept
*Wagashi from Kamuro --Another item for MIL.
*Craft beers Minoh Beer : Minoh beer can also be found in some bars and restaurants around Japan
*Yuzu Marmalade from Todoromi marmalade I've given these away and they've loved it!
*Madame Brulee by Madame Shinco
*Epinard's Truffle au Chocolat
Kochi: yuzu, red bell peppers
Tokushima: sanuki udon
Taco rice kits
in most Department stores in Japan : some info in Japanese only (sorry!)
*wagashi (japanese confection) from Chikujian
*char siu bao (buns filled with sweet char siu)
*European style sweets from Henri Charpentier
*Teas from (especially 728143) Lupicia teas
*Fusion style sweets from Malebranche
*Arare (rice crackers) from Ogurasanso
*MUJI teas, pens, curries, etc.
*culinary lavender from Ali'i Kula Lavender
*dark chocolate dipped shortbread from Big Island Candies
*assorted soaps from Bubble Shack Soaps (I usually buy these from Target)
*assorted soaps from Filthy Farmgirl Soaps
*Mango Maui tea from Hawaiian Islands Tea (Can be purchased at most supermarkets in Hawaii)
*assorted shortbreads from Honolulu Cookie Company (not as good as Big Island Candies but available on Oahu)
*teriyaki marlin jerky from Marlin Fish Jerky (can be found in most supermarkets & Costco)
*anything whole bean from Peet's Coffee (I usually buy them from Safeway)