In fiction writing, capturing colloquial accents can add color–although note that overdoing it might make things a bit challenging for the reader, if the dialect is a strong one.

I departed to renew my search its result was disappointment, and Joseph’s quest ended in the same.

“Yon lon gets was un’ war! observed he on re-entering. “He’s left th’ yate at t’ full swing, and miss’s pony has trodden dahn two rigs o’ corn, and plottered through, raight o’er into t’ meadow! Hahnsome-diver, t’ maister ‘ull play t’ devil to-morn, ad he’ll do weel. He’s patience itsseln wi’ sich careless, off craters–patience itsseln he is! Bud he’ll not be soa allus–yah’s see, all on ye! Yah mun’n’t drive him out of his heead for nowt!” –Emily Bront’, Wuthering Heights

However, if you are creating characters whose first language is not English, don’t go overboard in spelling their words as you thing they would sound. The effect may come through as ridiculing of the group the character represents, as well as making the dialogue difficult to read. This isn’t to say you shouldn’t convey foreign accents at all; just use moderation. A dropped letter here and a misused word there will usually be effective enough.

If you are quoting a real-life individual who happens to have an accent, either foreign or colloquial, it is better not to try to reproduce the accent phonetically at all, unless it has some direct relevance to the story. Direct quotes must include the exact words used, but you do not have to carry this to the extent of reproducing intonations.

With regard to style of speech, it is important to make your fiction characters talk realistically. You should have a firm handle on the rules of grammar, but you obviously don’t want to put perfect diction into the mouths of characters who are meant to be uneducated or rustic.

Every night now I used to slip ashore toward ten o’ clock at some little village, and buy ten or fifteen cents’ worth of meal or bacon or other stuff to eat; and sometimes I lifted a chicken that warn’t roosting comfortable, and took him along. Pap always said, take a chicken when you get a chance, because if you don’t want him yourself you can easy find somebody that does, and a good deed ain’t ever forgot. I never see pap when he didn’t want the chicken himself, but that is what he use to say, anyway. –Mark Twain, The Adventures of Huckleberry Finn