The calls are among those highlighted in a campaign called Keep the 999 Line Free For Me, by South Western Ambulance Service NHS Foundation Trust.
The trust said it often received 999 calls from people with minor injuries and even from those trying to get help for animals.
The campaign is running throughout the winter and encourages people to question whether they need to ring 999 or instead call the NHS 111 service or seek advice from a pharmacist or GP.
Hard-hitting posters show people in real emergency situations who do need the 999 service.
The trust, which covers Cornwall, Devon, Avon, Dorset, Gloucestershire and Wiltshire, is receiving 2,500 calls every 24 hours, which it says is an unprecedented number before the Christmas peak.
Deputy clinical director Adrian South said: “It can sometimes be difficult for people to know where to turn when they are worried about their health, particularly when they feel that the issue is too urgent to wait to see their own GP.
“If someone’s life may be in danger with a condition such as severe chest pain, shortness of breath, unconsciousness or following a serious road traffic collision or injury with uncontrollable bleeding, they should call 999.
“If the condition is less urgent then the NHS 111 service is a fantastic source of advice, and can direct people to a wide range of NHS services including pharmacies, GPs, minor injury units and walk-in centres.
“At the moment we are dealing with an unprecedented level of demand. It’s important to consider that every time we deal with a call which is not an emergency, it may delay our response to patients who are severely ill or injured; those cases where every second counts.”
The trust said examples of when an ambulance should be called are when someone is unconscious, not breathing, suffered a heart attack or stroke or has uncontrollable bleeding.
• Cat in the road
Caller: There’s a cat in the road. I think it’s dead, it is.
Operator: Are you calling about a cat in the road?
Caller: Yeah, yeah.
Operator: I’m sorry, we only deal with humans.
Caller: Oh right, sorry. I just wonder if I got the right number. Well, what number do I ring?
Operator: I don’t know, really. If you think it might be alive still, you could probably call the RSPCA.
Caller: Okay, I’ll give them a ring when I get into work.
• Directory enquiries
Operator: Ambulance service, what’s the address of the emergency please?
Caller: Um, well it’s not an emergency really. I can’t get through to the operator or directory enquiries. What’s the number of directory enquiries please?
Operator: Sorry, you’ve rung 999.
Operator: This is emergency services.
Operator: Is there a medical emergency there?