And, this is probably obvious, but there are numerous places to shop online overseas and have things sent to you, or companies that will ship the items to you in Japan instead. Be careful of import taxes though - anything leather especially, like shoes, or more expensive items might set you back quite a bit (check the link for more details on that).
(Most of the stores I've listed below are online sites only available in Japanese - you can use a browser translation tool or something like Rikaichan or Rikaikun to help you navigate.)
If you're looking for outdoor gear (clothes and/or shoes), you can find an extensive list of stores and brands here that sometimes do carry larger sizes.
Men and Women
Uniqlo carries some "plus size" clothing in its online store (up to XXL), for women and men.
Isetan has an online tall size (166-175cm) women's shop and also plus size shops for women.
Isetan also offers a tall and plus size store for men online. (If you live near an Isetan you might want to check out the store also.)
Aoki, a store with shops across Japan that focuses on suits and formal wear, has tall and plus size clothing for men and up to 3L plus size for women (link is to online store). The women's selection isn't as extensive as the men's.
Cecile (online) offers plus size clothes for women, men, teens and kids. Also has larger size bras.
Polopony (online store) has some larger sized tshirts and athletic wear.
Ito Yokado has a selection of plus-size clothes (thanks to Meredith for suggestion).
Tokyo: "Comme ca in Shinjuku store also has some great European sized clothing for women, men, and children. I also surprisingly stumbled upon some elegant, yet pricey, plus sized clothing (non-straight sizes) in one of the numerous store boutiques in Takashimaya in Shinjuku."
Nissen has a tall size online women's shop.
Rope is another Japan-based store that offers tall women's sizes online.
LLQueen focuses specifically on women's plus size clothing (online).
Chayclub also sells women's plus size clothes online.
Shimamura, a fashion store located around Japan, reportedly has some plus-size clothes (thanks -chai- for the tip!)
If you live in a major city with a Costco, you might want to check out their selection (thanks Bruce for the tip!)
Though this is technically ordering online, J.Crew, which used to be in Japan, has a Japan store and ships to Japan, and offers tall and some plus sizes for women, and tall sizes for men. (They also have up to size US size 12 shoes for women, but if you get anything with leather, the import fees can be outrageous.)
L.L.Bean has some US sizing, according to Bruce, and good selection.
While on the topic of American sizes, Gap in Japan sizes with US sizes (some shirts might seem a bit smaller, but overall they are usually the same). You can locate a Gap near you here. Gap Japan will also be opening an online store in October 2012, for those of you who don't live near one.
Zara has some tall-size clothes, including dresses and maxi-skirts. Ashleylaurent recommends sizing up if you shop here.
Aeon (shopping mall) also has some larger sizes. (Thanks to Haikugirl for the tips).
Tokyo: Haikugirl recommended British store Next, and Ashleylaurent suggested Topshop in Shinjuku for European sizes for taller women and men. Meredith also recommended Smileland in Shibuya.
Tochigi: Stacy suggests Sanki, "it has cheap clothes with labels that read XXXL. That size sometimes fits, and I am about a size 12 US." She also says Sanki is located elsewhere.
John suggested this Kanto-area store for men's plus size clothes:
"There is a shop that sells dress shirts, polos, and suits for plus size men (actually all size men). It's called Sakazen and there's quite a few around Tokyo. The stores generally have like 5 or 6 floors. The prices are fairly cheap, but some floors have more "exclusive" brands which are slightly overpriced. It's worth a visit."
Sakazen also appears to have an online shop.
MD (Mido) carries plus size men's clothing, up to 8L.
Kansai: Big and Tall (Thanks to Blueshoe for the tip).
If you have anything else to add, even if it's regional, let us know!