A couple of times a week I come across an online forum with people who are wobbly about the use of commas, so let me set this straight: Should the comma be used to indicate syntactical relationships, or should it mimic pauses in speech?
The answer is yes.
We'll start with syntactical conventions. And let's keep our focus on conventions and not talk about rules; all punctuation is convention. Some are relatively trivial. In the United States we use double quotation marks to introduce a quotation and close; in Britain they use single. In the U.S. we use a period with Mr. In the U.K. they omit the full stop. You'll just want to observe the conventions your intended reader is familiar with.
I'll take a moment to suggest that you could, FOR FOWLER'S SAKE, STOP CLAMORING ABOUT THE OXFORD COMMA. The serial comma, the final comma in a series, is endorsed by the Chicago Manual of Style, omitted, except when needed to avoid ambiguity, by the Associated Press Stylebook. I use either, depending on the house style of the publication I'm editing for, and you should do the same. You are not a paragon of virtue and cultivation if you prefer the Oxford comma, and you are not a stout-hearted freethinker if you omit it. Just shut up.
Observing the syntactical conventions enables you to make your meaning clear. Using a comma when the conjunctions and, but, and or introduce an independent clause assists the reader in identifying separate thoughts, particularly with longer constructions: I am merely acquainting you with the conventions common in formal writing, but you are free not to follow them if it suits your purpose.
Setting off appositives and nonrestrictive clauses with commas allows you to add information without gumming up the main thought: You, the writer, whose job is to make choices, must always keep in mind your reader.
It will make sense for you to use the comma as in common practice, with dates, introductory phrases, and the multiple other instances enumerated in style guides.
But yes, there is also something to a freer use of commas to indicate pauses as in speech. Punctuation was invented in antiquity to indicate pauses for readers of a text. David Crystal, in his history of English punctuation, Making a Point, quotes Richard Mulcaster's The Elementarie (1582) that the period "in reading warneth vs to rest there, and to help our breth at full."
You can consider the standard punctuation marks, comma, semi-colon, colon, and period, as the equivalent of musical rests for reproducing the rhythms of spoken English, the comma the briefest and the period the longest. The comma has proved extremely useful in the effort to reproduce demotic speech, particularly in fiction.
But it requires some discretion, to avoid the hazard of beginning to sound like Henry James "Experience is never limited and it is never complete: it is an immense sensibility, a kind of huge spider-web, of the the finest silken threads, suspended in the chamber of consciousness and catching every air-borne particle in its tissue."
Discretion requires judgment, and judgment means decisions, so keep in mind Oscar Wilde's account of proofreading his own work: "In the morning, after hard work, I took a comma out of one sentence. ... In the afternoon, I put it back again."