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A literary agent I follow told the story of a long argument her autoreply had with a would-be author. She’d set up the outbound email while out of town and apparently an author who queried her with his book took offense to it. He replied back in frustration that he didn’t get a personal response. Her autoreply sent back another automated message, which he then in increasing anger kept responding to.

And, although it’s fine to include certain details (e.g. what you’re doing), it’s vital to keep it professional. After all, this email will be sent to anyone who contacts you – so it’s not the place for inside jokes.
Yes, I phoned a dentist office late in the day for a reinfected root canal problem and got a cutsy “humphrey bogart” fake reply on their voicemail — I thought it was extremely inappropriate for a business office to use something like this. It was hard to find it funny, especially because while calling me “sweetheart” and all that, the message didn’t actually tell me when they might return my call (later that day? Next day? Next week? Never?) nor did they offer any options for emergency contact with another dentist.