When is it appropriate to end a question without a question mark?

Basically, if I ask a rhetorical question, it's not really prompting for an answer. Does that mean it should not end in a question mark?

Here are two examples:

• "What's New" used as a title for a section.
• "Who wants to reinvent the wheel." This is meant to be rhetorical, so is a question mark correct?

Solution 1:

The "What's new" example you provided is not necessarily a question, it can be a statement as it was something like "Here you can find what is new", so it doesn't obviously need a question mark. Of course you can also name the section (of a site, for example) as "What's new?" and in that case it's legit to use the question mark.

Regarding Rhetorical questions, they would need the question mark because they are questions. Still, the page that I linked explains that they can be followed also by a full stop or an exclamation mark, depending on the context where they are being used.

See for example:

• Wasn't that game incredible!
• Why are you so stupid?

Solution 2:

In formal writing, even rhetorical questions must always end with a question mark, so says Fowler and probably most other style guides. In informal writing, and perhaps with certain short questions that have become fixed expressions, a full stop could be used instead. I believe you will often find how do you do and what's up written with full stops.

I also agree with Alenanno that what's new could be a relative clause or an indirect question, which do not affect the status of the whole sentence with respect to question mark or full stop. Only a direct question can be a rhetorical one, and only the main clause counts for that—the following ones are all indirect, except the first:

Who wants to reinvent the wheel? — A classical rhetorical question; answer: "no-one!".

I wonder what I should do. — "I wonder" is just a statement.

I'd like to know what's new. — "I'd like to know" is also a statement.

Could you tell me why she left? — The question mark is there because the main clause is a question: "could you ...?"

Solution 3:

The Chicago Manual of Style, fifteenth edition (2003) identifies three distinct categories of questions that do not take question marks, at least in some instances: indirect questions, indirect one-word questions, and courtesy questions. Here is Chicago's discussion of these three exceptions to the usual pattern of ending questions with question marks:

6.72 Indirect question. An indirect question never takes a question mark.

[Relevant example:] How the two could be reconciled was the question on everyone's mind.

6.73 Indirect one-word question. When a question within a sentence consists of a single word, such as who, when, how, or why, a question mark may be omitted, and the word is sometimes italicized.

[Relevant example:] The question was no longer how but when.

6.74 Courtesy question. A request courteously disguised as a question does not require a question mark.

[Relevant example:] Will the audience please rise.

Actually, all of the examples that Chicago gives for each of these categories are relevant, but I've included just one from each category to provide a clearer sense of what the manual is talking about in each case. To see the other examples, you'll have to borrow or buy the book.