For the Famicom/NES, I don't know. I do know that the NES is a strange beast where the power supply actually supplies stepped down (way down) AC to the system, and the system has the rest of the DC conversion circuitry inside the console. I don't know how the Famicom did it. If the Famicom did it radically different, you won't want to blindly give it electricity from the NES power supply.
Also, unless you want to do some sort of weird video conversion with the RF output, go with an AV Famicom. With the proper power supply, that will work on American TVs most easily. You know about channel 3 or 4 in America? Japan does it differently somehow. But RCA AV jacks are standard between the countries.
The Dreamcast. bseb2003's example is probably right. If I'm not mistaken, Japan's wall outlet electricity is 100 volts AC. America's is roughly 120 volts AC at max, but lots of places never see the full 120. In fact, at work we always refer to our stuff as working on 110 or 115 volts AC because that's what usually comes out of the wall.
What's probably going on is that the Japanese consoles have the same transformers in the power supplies or internal power boards that the US consoles do. They just label it differently. I don't have any import consoles of my own, but I've never heard of somebody burning out their Japanese consoles in America just because they didn't use a 120 to 100 volts AC stepdown converter.
EDIT: for the Famicom. I couldn't find anything better, but this page has a little bit of information.
http://forums.benheck.com/viewtopic.php?t=24566&sid=cd622e767f48000139d2cec3bf8bcb82 I hope you have electronics knowledge because you're going to have to give it 10VDC, 850mA. The 850mA is the minimum. If you find a replacement that's rated higher, it's okay. Just don't go under. And definitely don't go over on the 10 volts DC. mikeskates at the bottom of the page did have an interesting post, though. An AV Famicom runs off of the NES 1 power supply. That's interesting, but without knowing why, I wouldn't recommend doing that. It might be just fine to do, but it might just kill the system in the long run instead.