Chinatown! Spanning several city blocks and centered at de la Gauchetière and St-Laurent is Montreal's Chinatown. There are dozens of vast Chinese grocers selling everything from smoked duck to chess sets. If it's Chinese, you'll find it here. On Sundays, the district has a marvellous bazaar-like atmosphere. Grocers extend their stores onto the sidewalk with fresh fruits, imported canned goods, and crates of thousand-year-old eggs (actually, eggs which have been potted for about a month). You could probably pass an entire afternoon wandering around, so plan accordingly. Champ de Mars Metro station is a good place to start.
Japanese and Korean
382 Victoria at Sherbrooke, Westmount (Vendome Metro)
6151 Sherbrooke W. at Beaconsfield, N.D.G.
Miyamoto is the only game in town for genuine Japanese articles, although the Korean Grocers (that can't be their real name!) comes pretty close. Miyamoto has every variety of Japanese noodle you could want, with the only exception of fresh soba that you find in convenience stores in Japan (although they do have frozen udon.) They have a good frozen section and a good selection of sauces and condiments (even that fiery bean paste, tôbanjan.)
The Korean grocer also has a fantastic selection of garlicky, chili-drenched Korean sauces and also has a large frozen section. Get large jars of Kim chee here, as well as Korean barbeque sauce for your next bulgogi, for which you can even buy the frozen beef.
European, Greek etc.
In a word, St. Laurent Blvd. (formerly known as The Main.) Little Italy begins at the upper end, from Jean Talon St., and progressing down towards the city center you'll pass through Portuguese, Greek, Spanish, and many other ethnic neighborhoods, ending up in the so-called Latin quarter down near Berri-UQAM. You'll find a couple of huge delicatessens and European markets right around Schwartz's. Again, make an afternoon of it, starting at either end of The Main. The 55 bus runs South to North. The Metro runs roughly under St. Denis street to the east.