Strunk & White are quite clear on the matter.
5. Do not join independent clauses by a comma.
If two or more clauses, grammatically complete and not joined by a conjunction, are to form a single compound sentence, the proper mark of punctuation is a semicolon.
Stevenson's romances are entertaining; they are full of exciting adventures.
It is nearly half past five; we cannot reach town before dark.
It is of course equally correct to write the above as two sentences each, replacing the semicolons by periods.
Stevenson's romances are entertaining. They are full of exciting adventures.
It is nearly half past five. We cannot reach town before dark.
This interesting page cites an excellent quote crediting an author but no specific work. I think it sums things up nicely.
I have grown fond of semicolons in recent years. . . . It is almost always a greater pleasure to come across a semicolon than a period. The period tells you that that is that; if you didn't get all the meaning you wanted or expected, anyway you got all the writer intended to parcel out and now you have to move along. But with a semicolon there you get a pleasant little feeling of expectancy; there is more to come; read on; it will get clearer.
— Lewis Thomas
So what then, are we to make of this?