There are two issues with using your appliances in Japan.
One is whether the plugs will fit the outlets. Japanese outlets are similar, but not identical, to North American outlets.
In particular: Most North American appliances these days come with polarized plugs, in which one prong is longer than the other. Japanese appliances have two prongs of the same size and shape as the *smaller* prong on a North American polarized plug. The upshot: If you have a polarized plug on your North American appliance, it will NOT fit into a generic Japanese plug. (I've seen some Japanese outlets that are designed to accept polarized plugs, but these are the exceptions, and you can't count on finding them.)
If you have a three-prong plug on your North American appliance, it also will not fit into a standard Japanese outlet, as these only have two holes.
So if your plug is polarized or three-pronged, yes, you need an adapter.
The other question is whether your appliances will work at Japan's 100 Volts, which is less than the North American standard of 120 Volts (and if you're in eastern Japan, 50 Hz for the frequency rather than 60 Hz). [To adjust for voltage differences would require a transformer, not just a plug adapter.]
If you've got a typical iron and hair dryer, they should be fine at this lower voltage. Your appliances might indicate what the input range of tolerated voltages is, but regardless, unless there's some fancy electronics in these things, I don't think there's a way these the lower voltage would cause problems in this situation. (Of course, since I pretty much never iron my clothes or use anything other than a towel to dry my hair, I've not actually done this.)
You can find some information on Japanese electrical service on this web site at:http://www.japan-guide.com/e/e2225.html
For electricity around the world, check out:http://kropla.com/electric2.htm