Russell's post about MURAKAMI Ryuu's gag rhetorics (you should probably go read it) reminded me of this joke from Crayon Shin-chan, which is rapidly becoming my prime source of linguistic data, I just realised. Remember, right to left:

Masao: あいちゃんのことを想うあまり眠れない夜が何日も続いたりする…
Kazama: (thinks) 不眠症か…かわいそうに…
Masao: …夢をよく見るよ
Kazama: ぐっすり眠っとんのかい

Masao's first line would be interpreted by any reasonable person as "I'm so hung up on Ai-chan that I go without sleep for nights on end...", and Kazama thinks "Insomnia... poor guy..."

But then Masao's second line (literally "I have dreams about [X] a lot") reveals that his first line was, in fact, only part of a sentence -- the "[X]" in my translation there. In other words, he's saying "I keep dreaming about being so hung up on Ai-chan that I go without sleep for nights on end", a gag which, in English, doesn't work (except maybe as surrealism).

It works in Japanese, though, because (a) Japanese modifiers (including entire clauses) come before the head noun, and (b) the verb forms used in such clauses are the same as the verb forms used in main clauses. (Although this wasn't the case in classical Japanese -- there was a separate form, known as shuushi-kei (終止形), for sentence-final verbs, but that's since been entirely replaced by the rentai-kei (連体形), which was originally the only form for modifying verbs -- although now this new multipurpose shuushi-kei has been renamed rentai-kei just to keep time travellers on their toes.)

On the other hand, the structure of English allows us to make jokes like "I thought it was a great movie... for me to poop on!", so we needn't feel too deprived.