Punctuation for the phrase "including but not limited to"

My choice would be:

There are many activities, including, but not limited to, running, jumping and swimming.

The comma before including shows that a new clause, even if it’s a non-finite clause, is to follow, and the comma before but and after to, indicates a weak interruption to that clause. The comma between running and jumping shows that the two are to be read as part of a list, but no comma is required after jumping, because and makes it superfluous.

"including but not limited to" is lawyer-speak, and comes from a lawyer's need to make sure that no one can ever, in any way, under any circumstances, think that "including" is all-inclusive. Merriam-Webster online says "including" means "to have (someone or something) as part of a group or total : to contain (someone or something) in a group or as a part of something : to make (someone or something) a part of something." So "including" has as part of its definition the fact that it is not all inclusive. Therefore "including but not limited to" is redundant (unless you are a lawyer writing a contract). Just use "including."

Comma use is subjective and in most, but not all cases is a style choice. The only place in that sentence where commas are required is in the list at the end (running, jumping, and swimming). The comma that I've used before and is called an Oxford comma and not all speakers feel it's necessary to include it, so that's a style choice as well.

I place punctuation according to how I want the sentence to be read whenever it's not an issue of proper grammar.

For effect I might say:

There are many activities, including, but not limited to, running, jumping, and swimming.

That slows down the tempo.

As for the dashes, I don't think they're appropriate. If you want to use a colon, it would be more like this:

There are many activities, including but not limited to: running, jumping, and swimming.

But all of the following are grammatically correct:

There are many activities, including, but not limited to, running, jumping, and swimming.
There are many activities, including but not limited to, running, jumping, and swimming.
There are many activities including but not limited to running, jumping, and swimming.
There are many activities, including, but not limited to, running, jumping and swimming.
There are many activities, including but not limited to, running, jumping and swimming.
There are many activities including but not limited to running, jumping and swimming.

I believe that the comma before "and" IS necessary, as it is the difference between doing either activity separately and doing both at the same time.

There are many activities, including, but not limited to, running, jumping and swimming.

1. Running
2. Jumping and swimming (however you would do that... try this syntax with something that actually makes sense to understand my point)

There are many activities, including, but not limited to, running, jumping, and swimming.

1. Running
2. Jumping
3. Swimming

I recall seeing a discussion about a comma before an "and" some time back and this was the conclusion there.

Sadly, the system here doesn't allow me to post this as a comment because of lack of reputation.