Going to school in Florida the most classical education I ever got was reading Bulfinch's Mythology in 9th grade. World history (same year) was bare-bones, with about two days on the Greeks and Romans and only a handful of individual people named.
Reading older books it seems like it was important for Westerners to know a lot about Romans and Rome, and know a lot about the religion and language. When did that change? Who said that classics weren't important anymore?
Mod note: please don't clutter up the thread with "but they still do". The question is obviously when and why Latin classes stopped being ubiquitous.
Here is a link to an article from 1892 in which Harvard College explains how its examination (for admission) process works, and why it allows certain students to substitute an examination in another field for knowledge of Greek and Latin. (Although it's a narrow exception that won't get you out of also knowing French and German).
http://www.theatlantic.com/past/docs/issues/95dec/745/greeno.htm
In 1900, the only admission requirement for my state university was a knowledge of Greek. (Although implicit in that requirement was the idea that everyone who spoke Greek would have first learned Latin, and a lot of other subjects, just because that's how the schools that taught Greek were organized).