conjunctions - When to use a comma before "and"

I often see people on the Internet using a comma before and in many cases (not adversative cases). Is it ok? In my language it is stricly prohibited to use a comma before an and except for adversative cases or when an apposition is in the front of that and.

Examples (which I consider not ok):

He is a great player, and he prefers to play Counter-Strike.

John joined the Army, and George joined the Marines.

What I consider exceptions:

Yes, and what is the problem?

I called John, my brother, and now I’m speaking with him.

Answer

From the Oxford Guide to Style 2nd ed section 5.3:

Use the comma to join main clauses that are semantically related,
grammatically similar, and linked by one of the coordinating conjunctions
and, but, nor, or, and yet. Such clauses are joined by a comma if they
are too long, and too distinct in meaning, to do without any punctuation
at all, but not separate enough to warrant a semi-colon:

Truth ennobles man, and learning adorns him.

Cars will turn here, but coaches will go straight on.

I will not try now, yet it is possible I may try again in future.

It may be omitted when the clauses are short and closely linked:

Do as I tell you and you'll never regret it.

Dan left but Jill remained.

I will not try now yet I may in future.