There are also some countries which haven't yet been allocated Krause numbers (China is one example I can think of). In such instances, the numbering system of another catalogue is used; this is distinguished by referring to "KM/Y numbers" or "KM/C" numbers. The "Y" refers to the book "Modern World Coins" by R.S. Yeoman; the "C" refers to "Coins of the World 1750-1850" by W.D. Craig. Y and C numbers are gradually being replaced by KM numbers, but this is another means by which "Krause numbers" can change.
Krause has a website, NumisMaster, kind of like an online version of the catalogues. You have to register with them (for free) to look up Krause numbers, and you have to pay a monthly or annual subscription fee to look up mintages and catalogue values.
There's also DVD versions of the catalogues. But watch out for bootlegged Russian copies on CD/DVD; the quality is allegedly quite good, but they're still illegal.