Addicts (usually but not always homeless) with all sorts of drug/alcohol caused health problems that they don't manage. Not to mention overdoses/too drunk to move.

Medically fragile elderly people trying to live on their own when they shouldn't be. Frequent falls with injuries, etc.

A friend of my mothers was in and out of the ER and med/surg floors for months with mysterious cardiac symptoms that ended up being a new reaction to a medication she'd been taking for years.

People who are just psychologically, hmm, needy and looking for attention. When I worked on an ambulance there was a lady who'd call weekly because she said her blood pressure was high (it never was) and we couldn't refuse to transport her.

And more...