Great question. There might be better examples, but let's look at one of the most famous poems, "Thoughts in the Silent Night" [1] by Li Bai:

  床前明月光，
  疑是地上霜。
  举头望明月，
  低头思故乡。

"Translated" word for word, it's something like

  Bed before bright moon shine
  Think be ground on frost
  Raise head hope bright moon
  Lower head think home

Note that it doesn't even contain 我 ("I"). One can render it as:

  Beside my bed a pool of light—
  Is it hoarfrost on the ground?
  I lift my eyes and see the moon,
  I bend my head and think of home.

Or:

  Before my bed, the moon shines bright;
  Be it frost aground? I suppose it might.
  I lift my head, the moon to behold, then
  Lower it, musing: I'm homesick tonight.

Moser [2] offers these gems on Classical Chinese: "Forget it. Way too difficult. If you think that after three or four years of study you'll be breezing through Confucius and Mencius in the way third-year French students at a comparable level are reading Diderot and Voltaire, you're sadly mistaken. There are some westerners who can comfortably read classical Chinese, but most of them have a lot of gray hair or at least tenure." "Whereas modern Mandarin is merely perversely hard, classical Chinese is deliberately impossible. Here's a secret that sinologists won't tell you: A passage in classical Chinese can be understood only if you already know what the passage says in the first place. This is because classical Chinese really consists of several centuries of esoteric anecdotes and in-jokes written in a kind of terse, miserly code for dissemination among a small, elite group of intellectually-inbred bookworms who already knew the whole literature backwards and forwards, anyway."

Wikipedia says [3]:

"Classical Chinese is distinguished from written vernacular Chinese in its style, which appears extremely concise and compact to modern Chinese speakers, and to some extent in the use of different lexical items (vocabulary). An essay in Classical Chinese, for example, might use half as many Chinese characters as in vernacular Chinese to relate the same content." "Classical Chinese rarely uses words composed of two Chinese characters; nearly all words are of one syllable only. This stands directly in contrast with modern Northern Chinese varieties including Mandarin, in which two-syllable, three-syllable, and four-syllable words are extremely common." "However, even with knowledge of grammar and vocabulary, Classical Chinese can be difficult to understand by native speakers of modern Chinese, because of its heavy use of literary references and allusions as well as its extremely abbreviated style."

However, I don't have a neat example at hand... Anyone?

[1] https://en.wikipedia.org/wiki/Quiet_Night_Thought

[2] http://www.pinyin.info/readings/texts/moser.html

[3] https://en.wikipedia.org/wiki/Classical_Chinese#Grammar_and_...