Can I use a power adapter designed for USA in Japan?

What I do when I need confirmation is to check this website:

http://users.telenet.be/worldstandards/electricity.htm

It has an EXHAUSTIVE list of each and every type, the voltage and the countries that use them. It's been handy for some of the stranger countries I've been to and hasn't failed yet.

Myself, I have a multi-adapter. The only country it doesn't seem to handle is South Africa, which has 3 giant prongs - bigger than the UK ones!

It's worth noting that:

** Although the mains voltage in Japan is the same everywhere, the frequency differs from region to region. Eastern Japan uses predominantly 50 Hz (Tokyo, Kawasaki, Sapporo, Yokohama, Sendai), whereas Western Japan prefers 60 Hz (Osaka, Kyoto, Nagoya, Hiroshima).

In practice, the answer is "yes, usually." If it's OK in the U.S., there's a very good chance it will work without issues in Japan.

Japanese sockets are (mostly) physically compatible with American plugs, and although the nominal line voltage is lower in Japan (100V), the vast majority of modern electronics goods intended for American line voltage (110V) work just fine in Japan. Most DC power supplies have enough latitude that they handle the difference without problems. I've even corresponded with an electronics maker who confirmed this for his product, saying that most power supplies are intentionally designed with a big safety margin to handle brownouts and out-of-spec power anyway, and that the U.S.-Japan difference easily falls within this margin.

The other issue, frequency, is not a problem for most electronics, as they generally convert to DC immediately anyway (it may be an issue for older clocks or anything with a motor driven off of AC).

I've lived in Japan for a long time and used tons of U.S. electronics products here without problems. I think I've only ever had one thing which didn't work properly (an analogue synthesizer with a rare AC power supply that depended on the line voltage for tuning... the digital bits worked fine, but the sound was out of tune).

The item you linked to is a socket adapter, not a voltage converter. It will not convert Japanese standard electricity to UK standard electricity. Therefore, you can only use it with equipment that works over a wide range of voltages. Higher end electronic equipment (e.g. a laptop) and equipment designed for travellers (e.g. a travel hairdryer) might be okay, but you need to check carefully.

By the way, not all USB sockets are created equal. The USB socket of the travel adapter you linked to has a maximum output of 1A. That's not bad but if, say, you charge your iPhone from it, it might take longer than you expect.

You should be right to use the same adapter BUT check the voltage! There's a significant difference between the UK and Japan! See http://www.whichplug.com/uk-to-japan/

I can add to the above. U.K. 240v high current items such as hair dryers and kettles will not work in Japan but it is possible to buy travel types which have a voltage switch 240/120 these should work in the USA and Japan with the right plug adaptor.