Japanese shoe sizes come in two forms, S,M,L,LL or cm.
Womens shoe sizes (cm)
XS - 22.5
S - 23
M - 23.5
L - 24
LL - 24.5
The largest size women's shoe you will usually find is usually 24.5cm or LL (though some places stock 3L or even 4L). That's a UK 6 or US 8.
Men's shoes tend to go up to 28 or 29cm. You'll need to search hard or be lucky to find shoes over 27cm, although they are out there (especially in big foreign brand shops like the Nike store, and outlet centres).
If you have larger feet than this, or yours are an unusual shape (wide or flat) then your best bet may be bringing/having them sent from home. Or ordering online. Jonathan pointed out in the comments the existence of a Japanese online store called Kutsu no Hikari - check it out.
The average sized European man should be OK in Japan for clothes. Men over 5ft 11 might struggle with trousers but T-shirts, shorts and jackets should be mostly fine. One of our writers is well over 6ft but has no problem with T-shirts, and has even managed to find a few pairs of sports trousers almost long enough.
The portly gentleman, however, will have problems. Clothes are rarely above size LL (smaller than a Western XL), although there are specialist stores out there (can't comment on style or price).
Clothes for women are a little more tricky due to the different average body shape of Japanese ladies.
Those above a UK 12/14 or US 10/12 will have trouble. And those smaller ladies with ample hips, bums or boobs will also have problems.
Chain stores from the West such as H&M have started popping up, and sell the same catalogue of goods as at home, although they usually only stock a few pieces in larger sizes.
Another good thing to stock up on whilst at home, or to buy online, are bras. Those with boobs larger than a UK D will find it impossible to find bras here. And even those who can fit into Japanese bras may find them uncomfortable, which is another thing we will be looking at soon.