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)
Ukeian (silkie bantam egg sweets)
Hatcho Miso (red soy bean paste)
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
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.
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
Bigot (info in Japanese)
Tommy's An Bread
Ca Marche's patchwork bread
Le Dimanche pastries
La Pierre Blanche sweets
Saga: Ureshino teas, Karatsu sweets
Nagasaki: Ikkoko & Kakuni-manju, Kanzarashi, Castella & Chinese sweets, Mikanzuke, Garlic Sardines
Kochi: yuzu, red bell peppers
Tokushima: sanuki udon
Taco rice kits
Shima ra-yu (chili oil)-Ishigaki Island
Ko-re-gu-su (chili pepper steeped in awamori)
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)