Here in Korea, there are large signs at some bathhouses that say, "By law those with tattoos are not allowed in the bath", but in the five years I've been here, I've never seen it enforced. I've seen Koreans (obvious gangsters and non gangsters) and foreigners here with tattoos and no one ever kicks them out. At most, you'll get quite a few stares. I've been going to this one across the street from my house for years with no problems:
Public pools can be a bit different. I've never had any problems, but a Korean guy I know was asked to wear a rashguard when he swims, because some people were complaining about his tattoos.
Japan is strict, and most places (especially in cities) will not let you enter a bathhouse with a tattoo. A couple of years ago when I was traveling around the country, I had tattoos that could be covered with a single rash guard sleeve. It looked pretty discreet, and I had no problems. I think everyone assumed my arm was hurt. Now, it would be impossible for me to enter many of them.
If you ever go to Japan and want to experience the bathhouse culture, I recommend going to the mountain towns (I suggest Takayama). There are many free open air Onsen in the mountains, and there are no restrictions on who can bathe.
EDIT: Zankou, haven't you mentioned before that you lived in Japan or have visited a few times? I guess you already know about Japan then.