Asia World is one of the better supermarkets in the Dallas area selling East Asian products. While mostly geared toward the Chinese community, they also sell Japanese, Korean, Vietnamese, and Thai products. In the back they have fresh specialty meats and fish, including pigs' feet and live lobsters, things you won't find in your standard Tom Thumb. The produce section features Asian favorites like durian and papaya. There's an entire aisle dedicated to different kinds of instant noodles, and there are sizeable selections of teas and Asian snacks as well. (Come here for your Pocky, it's cheaper than other places.) You can also get cheap dishes and cooking accessories, and a lot of them are actually quite nice. And don't forget to check out their Asian specialty drinks near the produce section!
On weekends they will often have tables set up selling fresh meals and distributing samples. In addition, I believe you can sign up for cell-phone plans here, and they have a number of odds and ends like phone accessories and jewelry.
$20 minimum purchase is required to pay with credit card. People working there aren't the nicest, but it's a grocery store, so it's not like you'll require much assistance. Highly recommended.