Criminal Sentence 26: Don't Run On

From a water bottle I drank at the ballpark last night:

"We can all make a difference, please recycle."

Good sentiment; bad punctuation. This sentence is really two sentences that should be separated with a period, not a comma:

"We can all make a difference. Please recycle."

You can't put two complete thoughts together with just a comma. Wrong;

I love you, will you marry me?
He ate too much cake, he got a tummy ache.

Right:

I love you. Will you marry me?
He ate too much cake. He got a tummy ache.
He ate too much cake, so he got a tummy ache.
He ate too much cake and got a tummy ache.