Should it be "Guess what?" or "Guess what."?

It’s a statement, not a question.

I think it needs an exclamation point. It’s a statement, but it’s usually a very emphatic one.

Really? My understanding was that it was a question, since you’re technically asking someone to guess, even though that may not be what you actually mean. Of course I must admit I haven’t taken any english since high school (almost 5 years ago now!) so this definitely isn’t an answer, it’s more like a continuation of your original question… :)

Something I never thought of, I’ve always used a question mark.
Now that I think about it, a period is definitely more appropriate.

this sounds like jeruba’s area of expertise

I completely agree with @EmpressPixie.

I agree with EmpressPixie. If I were writing it in personal correspondence or in story dialogue, I’d write “Guess what!” If I were being ironic, I might just use a period, but this is no place for a question mark.

The response, however, would be “What?”

I also write “I wonder how you punctuate that.”—a statement, not a question.

Guess what! I don’t know.

This is from North Carolina State’s online writing lab

Question (from a film-subtitling company in Los Angeles): A friendly dispute has arisen at work: I contend that the phrase “Guess what” is a command and thus requires a period. My colleagues insist it is a question.

Answer: Who are these people? I didn’t think Californians ever insisted on anything. I thought they just “leaned weakly toward the possibility that . . .”

At any rate, you will be gratified (but not surprised) to hear that you are right, and they are wrong, wrong, wrong—or at least tilting in the wrong direction. “Guess what” is an imperative, which is conventionally punctuated with a period, not with a question mark.

This, of course, will not satisfy the insisters, who are likely to suspect that you have hired a grammatical ringer. To convince them of the error of their ways, you will have to toss them an analytical bone.

Here’s the rest of the story:

Imperative sentences in English are conventionally punctuated with a period, not with a question mark, but this, of course, begs the question whether this is an imperative sentence at all. Many seeming imperatives are actually simply colloquially short ened versions of interrogatives. Let’s compare two sentences that seem to be similar:

Know what(./?)

Guess what(./?)

The deep structure of “Know what” can be expanded to “Do you know what?” and “Do you know what?” is clearly a question. Furthermore, “Know what” could never logically be an imperative, since you can’t command someone to know something.

“Guess what,” of course, is different. You can clearly command someone to guess something, whether or not they choose to comply. And though “Guess what” could perhaps be expanded to “Can you guess what?” the inflectional pattern suggests that that’s no t what’s going on at all.

Let’s compare the inflectional patterns. “Know what” starts low and rises. This is what questions do. “Guess what” starts in the middle and stays there. This is what commands do.”

After reading @Harp‘s answer, I’ve decided I should have taken more (well, rather, any) english in college. ;)

If the speaker is trying to figure out what someone wants them to guess, then I would choose to go with a question mark.

Otherwise, I would probably put an exclamation point on since it seems to be expressing emotion rather than positing an answerable question.

When you say it, your voice doesn’t go higher at the end. That’s a good indication it is not a question.
I am with @EmpressPixie . Exclaimation mark.

GUESS WHAT! I think I have the answer! It’s an exclamation of something I have discovered! I am suggesting that you guess what I have discovered!