Here is a paper size chart I thought might be interesting: http://www.dpandi.com/paper/
Wikipedia also has some interesting info: http://en.wikipedia.org/wiki/Paper_size
A4 is roughly, but not exactly, equivalent to the "standard" US paper size of 8.5 inches x 11 inches. That's the size of spiral notebooks or looseleaf paper we often use in school, for example. A4 is more like 8.3x11.7 inches, or 210x297mm.
A composition book in the US is one of those bound books often with a marbled black-and-white cover which measures about 7.5 inches by 9.5 inches; it often has about 100 sheets (200 pages). B5 is somewhat close to this--6.9x9.8 inches or 176x250mm. A5 is a bit smaller, 5.8x8.3 inches or 149x210mm.
Sometimes I get taken in by notebooks with pretty covers and a low price (online), then I look at the size and realize, "Oh, that's kind of... tiny, actually." I'm not really into the very small notebooks, like the kind reporters in old movies have that fit in the palm of their hand for taking notes. That's maybe 2 inches wide by 3 or 4 inches high--something like an A7 or A8. Though, I do have some little tiny composition books with marbled covers which are about that size, and they are very cute--it's just hard to figure out what to do with them. They aren't very good for writing stories in, for example. In the past I used to always carry one around for writing down story ideas
as they came to me, but that hasn't been so necessary in the last few years, for some reason.