I saw a simple question in a comment on SE:
What if I told you there was a sci-fi and fantasy blog?
We have a blog?
But according to my English textbook, that question should be: Do we have a blog? So I just wonder, We have a blog? is a mistake or it's correct and has a different meaning from Do we have a blog?
What you noticed is an example of echo questions.
Normally, questions would follow the grammar you expect them to. They would contain an auxiliary "do" at the beginning; that kind of absorbs whatever inflection the main verb has. So you get something like this:
Do we have a blog?
However, there's a unique way of expressing surprise. That's where echo questions come into play.
A: We have a blog that contains awesome stuff.
Ms. B can answer this in two ways using echo questions:
B: We have a blog?
or
B: We have a what?
Do we have a blog?
. . . asks the direct question
We have a blog?
. . . asks the same question but adds a feeling of surprise to the statement. (The person who is asking the question just heard that they have a blog and is surprised by the statement)
For reference, I would recommend using an "Do we have a blog?" inquiry to find out direct information and using an "We have a blog?" inquiry when questioning a statement that may have surprised you.
If you start a conversation with somebody to ask this question, you would say
Do we have a blog?
If you are having a conversation with somebody and they happen to mention that "we have a blog" and you are a bit surprised to hear that, you can ask for confirmation by repeating the statement as a question:
We have a blog?
They are both correct English. As far as I am aware echo questions are not a formal construct (edit: by which I mean that they are not syntactically distinct) and both forms are perfectly acceptable on their own. They can be used sarcastically as well to feign surprise. To me, the key is that while the '?' distinguishes them as questions in written work, when spoken one can only tell the later is a question by an inflection in the intonation that is unwritten. While this kind of question is common in English, the use of intonation to convey meaning is not generally common in English, though it is in some other languages, e.g. Mandarin.
https://en.wikipedia.org/wiki/Intonation_(linguistics)
What I mean is, it makes perfect sense to walk into a room and say "John left already?" This is still the case even if you're not surprised that you don't see John and no one said anything before your question.
Perhaps another aspect is context in regards to how likely it is that you are to ask a question that way. That is, if you are going out with friends by train, even though no one has mentioned tickets you might say, "we have tickets?" or "you have the tickets?" while approaching the station. Adding the interrogative will often make your question more clear though, especially in cases with less context.
Edit: My examples here are so called declarative questions, which need not be (though are commonly) echoic.
"The guiding hypothesis in explaining the restriction is that questions must be uninformative with respect to the Addressee - a requirement that declaratives can only meet in certain contexts. The analysis predicts , correctly, that in addition to their familiar "echoing" function, rising declaratives may be used to question presuppositions and inferences taken to follow from the Addressee's public position, whether or not such inference finds its basis in a preceding utterance."
(17) [A&B are looking at a co-worker's battered and dented car]
A: His driving has gotten a lot better.
B's response:
a. Has it? I don't see much evidence of that.
b. It has? I don't see much evidence of that.
c. It has. #1 don't see much evidence of that.This skeptical reading of rising declaratives is well known, and is often assumed to be connected to their "echoing" function. But it would be a mistake to assume that rising declaratives are inherently skeptical (or inherently echoing, for that matter). Rising declaratives, like interrogatives, also allow for readings in which the Speaker is understood as routinely accepting the proposition expressed, as illustrated in (18), where the falling declarative is acceptable as well.
(18)
A: That copier is broken.
B's response:
a. Is it? Thanks, I'll use a different one.
b. It is? Thanks, I'll use a different one.
c. (Oh), it is. Thanks, I'll use a different one.
Declarative Questions
Christine Gunlogson
University of California, Los Angeles
Available here: http://journals.linguisticsociety.org/proceedings/index.php/SALT/article/viewFile/2860/2600
Edit 2: Realized that I did not directly answer the question. In short, "We have a blog?" is correct and does have a different meaning than "Do we have a blog?" In this instance it probably does indicate surprise as some other answers have mentioned. My reason for writing this answer was to point out that this is not always the meaning conveyed by this syntactic structure.
