There's a concept (inspired by a Metafilter blog post) of ask culture vs. guess culture. In "ask culture," it's socially acceptable to ask for a favor -- staying over at a friend's house, requesting a raise or a letter of recommendation -- and equally acceptable to refuse a favor. Asking is literally just inquiring if the request will be granted, and it's never wrong to ask, provided you know you might be refused. In "guess culture," however, you're expected to guess if your request is appropriate, and you are rude if you accidentally make a request that's judged excessive or inappropriate. You can develop a reputation as greedy or thoughtless if you make inappropriate requests.
When an asker and a guesser collide, the results are awful. I've seen it in marriages, for example.
Husband: "Could you iron my shirt? I have a meeting today."
Wife: "Can't you see I'm packing lunches and I'm not even dressed yet? You're so insensitive!"
Husband: "But I just asked. You could have just said no if you were too busy -- you don't have to yell at me!"
Wife: "But you should pay enough attention to me to know when you shouldn't ask!"
It's not clear how how the asking vs. guessing divide works. Some individual people are more comfortable asking than guessing, and vice versa. It's also possible that some families, and some cultures, are more "ask-based" than "guess-based." (Apparently East Asia is more "guess-based" than the US.) It also varies from situation to situation: "Will you marry me?" is a question you should only ask if you know the answer is yes, but "Would you like to get coffee with me?" is the kind of question you should ask freely and not worry too much about rejection.
There's a lot of scope for rationality in deciding when to ask and when to guess. I'm a guesser, myself. But that means I often pass up the opportunity to get what I want, because I'm afraid of being judged as "greedy" if I make an inappropriate request. If you're a systematic "asker" or a systematic "guesser," then you're systematically biased, liable to guess when you should ask and vice versa.
In my experience, there are a few situations in which you should experiment with asking even if you're a guesser: in a situation where failure/rejection is so common as to not be shameful (i.e. dating), in a situation where it's someone's job to handle requests, and requests are common (e.g. applying for jobs or awards, academic administration), in a situation where granting or refusing a request is ridiculously easy (most internet communication.) Most of the time when I've tried this out I've gotten my requests granted. I'm still much more afraid of being judged as greedy than I am of not getting what I want, so I'll probably always stay on the "guessing" end of the spectrum, but I'd like to get more flexible about it, and more willing to ask when I'm in situations that call for it.
Anyone else have a systematic bias, one way or another? Anybody trying to overcome it?
(relevant: The Daily Ask, a website full of examples of ways you can make requests. Some of these shock me -- I wouldn't believe it's acceptable to bargain over store prices like that. But, then again, I'm running on corrupted hardware and I wouldn't know what works and what doesn't until I make the experiment.)
FWIW, among my friends--whom I might describe as "polite askers" or "assertive guessers"--it's common to ask "does anybody want to split this with me?" That way, you're both asking for what you want (more of the thing) and making an offer in a guess-culture-compatible way. It's easy for other people to accept, because now by taking it they're not preventing you from having it. If no one does, you can be reasonably confident no one else actually wanted it.
A variant on the same thing is: "Would anyone else like this?" which is a shorter version of the offering ritual that TheOtherDave described. Because it's skipping most of the ceremony, it's much askier, but it's still not polite to say "yes" and take the thing, because you'd be taking it out of the hands of someone who clearly wanted it. (An exception might be made if you hadn't actually had any of the thing yet, and said so.) But you can say "I'll split it with you," achieving the same result as the above.
Of course, this only works for plausibly divisible things. I've had a friend laugh at me--good-naturedly--for offering to split something bite-sized. Surprise, surprise: he's much askier, I'm much guessier.