Changing paragraphs is one small aspect of writing that I have seen few people feature on a blog or in a writing magazine or ezine. It may be that even writing instructors take it for granted that everyone knows when you should change to a new paragraph. Not necessarily so. Some of the above are pretty clear and something most writers would do automatically but others might not be so easy.
Note that the first three all contain the word new. It should be apparent that when introducing a new anything, you should start a brand new paragraph. Aha! There is that word new again. Hang on, as you'll see the word mentioned a few more times in this post. Much as I hate repetition, sometimes we have no way around it.
When a setting changes, it makes perfect sense to initiate an entirely different paragraph. it gives the reader a breathing space between settings, or places.
The point about using a new paragraph when a new person is speaking is one that many writers stumble over when writing dialogue. If Susie and Mary are having a conversation, begin a new paragraph each time there is a change from one character's dialogue to the other. It looks strange sometimes when you see lots of short paragraphs in a lengthy dialogue but it's a good rule to adhere to.
The last two are pretty self-explanatory. They might both be included under the fourth point.
There is another time when moving to a new paragraph is helpful. When the writer is making a strong statement, it is beneficial to set it in a paragraph on its own. It would be the same with something that might be of a shocking nature or particularly poignant. It is going to make the reader sit up and pay attention if it stands alone rather than being the end of the preceding paragraph.
When you're editing and revising your work, check your paragraphs. Do they measure up to the poster above? Or have you included too many topics in one long and convoluted paragraph?