In particular, older japanese houses and apartments are very poorly insulated (perhaps designed more for the loooong summer instead?). Most homes don't have central heating, and most don't have carpet on the floor, meaning that winter can be miserable.
The most famous is probably the kotatsu (the heated table). This table comes with its own blanket and you can spend hours curled up underneath it (eating mikan oranges!)
Another popular way to stay warm is the hot carpet. This is electric too, and plugs into the wall (like the kotatsu). They are even made in pet sizes!!
If you are outside the house, one way to keep yourself warm is with kairo (hand warmers which you shake to activate). They come in different shapes and sizes and some are backed with sticky paper so that you can put them inside your clothes (e.g. inside your shoes or on the back of your shirt).
If you are still feeling the cold, you could try microwavable shoulder warmers / stomach warmers / eye warmers...
Uniqlo (and recently other clothing manufacturers) make warm inner wear like Heat Tech... reasonably priced, in all sizes (for kids too) and colors, there is no reason not to own a couple of these.
(some 腹巻き even have pockets for your kairo!!)
How about warm woolen underwear...?
And of course, the traditional hot water bottle (yutanpo - 湯たんぽ)
Since there are so many ways to keep warm... and I haven't even started on all the toasty warm winter food (like nabe) and drinks (even available from vending machines!!)... there is no excuse for being cold this winter.
Are there any other ways you like to stay warm in Japan?
p.s. because many people use things like space heaters, kotatsu and electric carpets to keep warm, the risk of indoor fires is increased during winter. Make sure you switch off your electric devices after extended periods of use, and don't forget to install a smoke detector!! Safety first ;)