In what cases should I use a comma after "please"?

It is simply a matter of emphasis, which is why you can see it written both ways. For instance, if you had a visitor at your house, who was going to leave the house after you had left it, you might say:

Please don't forget to lock the door when you leave.

However, if this particular person had a habit of leaving the door unlocked, you would want to emphasize the "please", and could do it like so:

Please, don't forget to lock the door when you leave.

Which, when said out loud, has a louder "please" than the first example.

Basically, it emphasizes the importance of the request.

Also, if the "please" is at the end of a sentence, there must always be a comma, e.g.:

Don't forget to lock the door, please.

There is no strict rule, you are right. But inserting or omitting the comma after a leading "Please" can change the meaning of your sentence.

The comma is required in some cases.

A comma is almost always required before "please" at the end of the sentence.

Whether to use a comma or not depends on what you mean to say. "Please" can be a verb, an adverb or an interjection. When used to implore or request, it is an adverb modifying the verb of the requested action. The usage of punctuation (such as a comma) can change the meaning of the word by changing its part of speech.

"Please! Eat your broccoli."

In this case, "please" is clearly an interjection because it is set off by an exclamation mark.

"Please, eat your broccoli."

Here "please" is also used as an interjection but with a milder emphasis.

"Please eat your broccoli."

In this form, "please" is an adverb modifying the verb "eat".

Rule of thumb: When an adverb is separated from the verb it modifies by phrases or other adverbs, it usually should be offset by a comma. When the adverb is adjacent to the verb it modifies, it should not have a comma.

"Please eat your broccoli."

The adverb "please" modifies the verb "eat" and is adjacent to it, so a comma is not required. But a comma may be added if the word "please" has some special emphasis in this context or is a transitional word from another sentence.

"Eat your broccoli. Please eat your broccoli."

"Eat your broccoli. Please, eat your broccoli."

In the first couplet, "please" is a simple adverb, as before. In the second couplet, "please" is an adverb with special emphasis related to its context. That emphasis is conveyed by the comma. This is similar to the transitional usage I'll discuss next.

"Why do I have to beg? Please, eat your broccoli."

"Please" is the "begging" referred to in the previous sentence, so a comma may be used to convey its usage as a transitional adverb between the two sentences. But there is no hard and fast rule on this.

"Please, for the last time, eat your broccoli."

The adverb "please" modifies "eat", but the two words are separated by a clause which is offset by commas.

"Please, can you just eat your broccoli?"

The adverb "please" modifies "eat"; it does not modify "can". Since it is separated from its verb, there is a comma. Do not be fooled by the verb "can" which is unrelated to "Please". A comma is required here.

"Eat your broccoli, please."

Here the adverb follows at the end of the sentence and is not adjacent to the verb. A comma is required for clarity.

"Please, quickly eat your broccoli."

Multiple adverbs ("please" and "quickly") are both modifying the verb "eat", so the comma is needed to indicate that these are sequential modifiers. On the other hand, this could be interpreted as an interjection similar to "Please! Quickly eat your broccoli." Interpretation here depends on the context and the reader.

"Please quickly eat your broccoli."

Removing the comma from the previous sentence changes its meaning (and removes ambiguity). Now the word "please" is definitely an adverb, not an interjection. However, it is now modifying the adverb "quickly" rather than the verb "eat". The lack of a comma indicates the adverbs are not sequential modifiers, so we are left to interpret them this way.