1. There you go, you put the bad-mouth on others.

2. There you go again, you put the bad-mouth on others.

3. There you go. You're always forgetting things.
4. There you go again. You're always forgetting things.

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Do we have to use 'again' or not? Are both okay? Which one is commonly used? Otherwise, are both different in meaning?

See your other post about these.

Keeping the word "again" in there is a good idea for this particular expression.

Most of the time "there you go" is a phrasing meaning "you're right" or something similar.