I wonder why?

In form it is a statement, but in function it is a question.

It is a common convention to add a question mark if a statement functions as a question.

I agree with Emily. It does seem silly.

If you say "I'd like to know why it works that way," does it look better with a period or a question mark?

I'd like to know why it works that way.
I'd like to know why it works that way?

Possibly because "I wonder why" is somewhat ambiguous. It could imply "I wonder why it works that way." But, it could also imply "I wonder, why does it work that way?", a subtle but relevant difference, with "I wonder" functioning as an introductory or paranthetical clause. I suppose there really should be a comma if there's a question mark, but I never see it written that way, "I wonder, why?" Also, when spoken, I never hear a pause where the comma would be, so I could be completely wrong about all this, but at least it's a possibility.

PS - In English (and other languages) it is perfectly acceptable to form statements into questions simply through inflection of the voice (and adding a question mark when writing). Sometimes it implies sarcasm or a challenge, etc.

e.g., "Oh, and I suppose you are going to do it anyway, you stupid fool?"

oops, thats parenthetical, not paranthetical.

Although It is strongly preferred to not use a question mark in such a sentence, there is reason to do so. Question marks do not necessarily imply that a question has been asked, they merely imply that the speaker is in a state of confusion or curiosity. Therefore a question mark would be marginally acceptable in "I wonder why."

porsche says (correctly) that it is acceptable to convert a statement into a question by changing the inflection, but this is almost always done to create a yes-or-no question (and usually the questioner has a particular answer in mind): "I suppose you are going to do it?" "That's a fish?" "He's brought his mother?" I doubt very much that Truss means "Am I wondering why?"

"Eats, Shoots & Leaves" is poor grammar book, full of grammatical errors. Louis Menand wrote a funny and excellent review of it in The New Yorker: http://www.newyorker.com/critics/books/?040628crbo_books1

Punctuation isn't grammar, it's orthography. That's not just being pedantic, it's the essence of the question. In some cases -- such as semi-colons -- it serves to mark out function, in some -- such as exclamation points -- it serves to mark intonation, and in some -- and this is the case with question marks -- it marks both. To put a question mark at the end of something is to indicate not just that it is a question, but that it is pronounced with the rising intonation appropriate to questions. I might write "I wonder why" with a period, a question mark, or even an exlamation point, depending on how it would be pronounced if it were to be.

I would say that it depends on the context that Lynn Truss writes these three words: "I wonder why," because I would include the question mark if I know that she is asking a question with these words, and if it is cited, or if she is just writing these words objectively, not as a question, then I wouldn't include the question mark.

I'm guessing that she writes, "I wonder why," in wonderance about some aspect of EATS, SHOOTS, AND LEAVES. If I'm wondering about the context that Lynn Truss writes, "I wonder why," then I would include the question mark, but since I'm writing, simply, concerning the objective discussion of these words, then I could not include the question mark because the words, by themselves, might be broken down into an unrelated semantics, but it doesn't make much sense, to me, to write, "I wonder why," as anything else other than a question because that is the ultimate meaning of the phrase.

use no question mark; it is not a question.

I think the issue here is that people see a "question word" and automatically put a question mark at the end. In my last job I'd get emails with "questions" like these:
Please tell me which of these figures is correct?
I don't know what spreadsheet I should be using??
I'd like to know when the new version will be available???

Hang on, after reading some of those replies, maybe those question marks in my post above are correct after all. They're statements, but they expect an answer from me so they're questions too. Now I'm confused.

Chris, "Please tell me which of these figures is correct" is ambiguous, at least if you ignore the presence or absence of commas. Clearly, "please tell me, which of these figures is correct?" with a comma, would require a question mark. Interestingly, the verb "tell" is reflexive in the statement, but not in the question. The other two examples of yours are clearly statements.

I have a question.
Could you give me the difference between “I wonder” and “What if?”
They both sound similar at first, but I suspect a difference that I’m not seeing. Any input will be greatly appreciated.
Thank you, Mark.