Those annoying independent clauses

I frequently see independent clauses -- clauses that can stand alone as a sentence -- joined together haphazardly.

There are three basic ways to do it: use a comma followed by a conjunction, a semicolon alone, or a semicolon followed by a sentence modifier. A sentence modifier is a word or phrase that is not the subject or predicate but adds to the meaning of the sentence.

The Simply Study Guides website provides these examples:

Incorrect: The delivery boy knew he carried strange cargo, but still ventured off unafraid.

Correct: The delivery boy knew he carried strange cargo, but he still ventured off unafraid.

Incorrect: My math teacher doesn't know how to lecture, she should have remained a student.

Correct: My math teacher doesn't know how to lecture; she should have remained a student.

 [In my mind this previous example, known as a comma splice, is one of the most egregious grammatical errors. Okay, it just annoys me ear.]

Incorrect: Gregor has not changed physically; but has given himself an excuse to separate himself from the pain of previous experiences.

Correct: Gregor has not changed physically; however, he has given himself an excuse to hide from the pain of previous experiences.

You might ask yourself, as well, whether the clauses ought to be joined in the first place. Perhaps two sentences is better. Does the meaning require joining? Does it contribute to a more pleasing style? What will most help the reader grasp the meaning?

Having trouble recognizing independent clauses? The Tongue Untied has some examples, and offers this slightly different insight:

The independent clause is the main idea of the sentence. It is not dependent on another clause for meaning and context. 

Avoid using the description that the independent clause can "stand by itself" or "makes sense by itself."Many dependent clauses, when removed from the context of the sentence, make sense on their own. Nonetheless, they are dependent on the rest of the sentence for meaning and should not be evaluated outside of the sentence.

You really don't want to get between two grammarians.