I see them all the time, so I think they're okay. As with everything, though, I'd try not to over-use them. Usually I see them either when you're in a character's head or in dialogue.
They're OK. Incomplete sentences are a good way of controlling the pace and/or tone. I use them more in dialogue than in the narrative.
I'd say they are ok if you are using them stylistically, but if it just comes off as you being grammatically ignorant, people (pedants) may get upset with you.
Then the pedants get upset with a lot of terrific writers. Sentence fragments are quite commonly used by writers who are keenly aware of the "rules," but are also aware of the effects they're trying to achieve in their prose. Pedantry gets in the way of art an awful lot, and that's not the fault of the artists.
Never! Can't do it. I'm not serious. By all means, if a sentence fragment gives the right emphasis, go for it. You don't want to overdo it, of course, but fragments work very well in fiction when used judiciously. I would not recommend them for your Doctoral thesis, though.
I'll use them, and not just in dialogue -- I use them in first-person PoV stuff, too. Helps to establish a voice.
I used them in my recent post Garyk the Treasure Hunter and was accused of over-using them... so, I don't know. True, I did use them in narrative, but it was basically the character's perception of the scene, which would make it justified. I also see them quite a lot.
I use them during action scenes. When I need the pace to quicken, like pop-pop-pop. I use sentences like: A single gunshot. Punch. Dodge. Falling. There are alot of reasons to break the rules, pacing being one of them. ~ J.J.
I tend to use them a lot, and see no reason why they can't be used if you're using them well. They're common in dialogue a lot, but I do know someone who used them and made it so the incomplete sentences are an amazing tool to his writing.
Do it in dialogue too if the person is being interrupted... U'll be surprised how many times people are interrupted in real life conversations (especially the socially awkward.)
The opening of Dickens' "Bleak House" is rated by some as one of the greatest examples of literary style in English, and is completely in fragments -- incomplete sentences. One of the two narrators of Jon McGregor's "If Nobody Speaks of Remarkable Things" speaks entirely in fragments. As with everything else, be aware of the effect the way you are writing has on the reader. Fragments have a strong effect. Think of them like chilli, and the Dickens and McGregor examples as being like super-hot chilli con carne. Some people love them, but you'll sell a lot more chilli con carne if it's only got a little bit of chilli in it.
Look at Lee Child's Jack Reacher novels for an example done well. Short, snappy sentences are used in his books, and if it works for him, then in theory it can work for anyone. But as everyone has said, unless it's called for, don't overdo it (and use it well).
I think they are ok in dialogue but not in the general writing. They can be used to tie the story to a region or a particular dialect but you have to be very careful with that because only a few professional writers can pull it off. I have the opposite problem to this and that is the one were acedemics especially if they are English professors write fiction. To me they become too wordy and exacting intheir writing. The only exception to this, of the ones that I have tried to read, is Wallace Stegner.
Look carefully at the stuff you read. I bet you'll find fragments crop up in the general writing, too.
Agree with all those who say it's a stylistic choice. I write a lot of first person POV and commonly employ sentence fragments to make it feel sort of stream of thought. Also acceptable in dialogue. And in message board posts, if that last one I used means anything
Oh yes. I bet if you copy and pasted any recent book into Word, it would light up green like a christmas tree. For example, one chapter in a Douglas Adams book starts like this: If you look hard enough, you'll find plenty of fragments in popular writing. ~ J. J.
A good example of its use in narrative. If the reader is enjoying the read then they probably won't even notice the fragments, which I suspect is why some people think they can't be used there -- they just haven't noticed them.
We don't always talk in complete sentences. IMHO dialog should be written as you'd expect the character to speak under the situation he is in. Keep dialog comfortable if you can't keep it gramatically correct. I don't see how you'd keep characters "Real" otherwise. If you are writing a Cowboy tale you will need to slip into the brevity of "Cowboyese." "Reckon you're right" rather than "I'm sure you are correct." I tend to follow the same direction with narration. Follow the tone of the story. If the narrator is a cornpone hick like I am, I'd expect him to narrate like he speaks. I hate to listen to a book on CD where the reader doesn't understand the dialect. These are my amateur comments. I'm a wannabe.