It sort of depends upon where you practice, what type and size of agency you work for, and how unstable your patient population is.
You might get lots of calls for stuff that could get taken care of during regular business hours. If that is happening talk to your manager about it...that's a pretty expensive way to meet basic needs and suggests that perhaps good teaching is not occurring in the home.
If you work for a hospice that has more than 100-150 patients you will regularly get calls for legitimate symptom and support issues. Family will call in the middle of the night because they are tired and worried and need someone to tell them that it is okay to give the morphine. People who need the next step in the POC to manage the issues they are dealing with.
The higher the agency census the more frequent the off shift deaths. Ask about the number of deaths/week and see if they keep data on time of day or day of week. It is weird sometimes how there are patterns where there shouldn't be.
If you have a medically unstable patient population (home infusions, complicated wounds, tubes/drains, artificial airways, etc) you will get calls for equipment issues or questions. You will have to visit to change bags and replace dressings, and unplug stuff.
The thing we most often call Hospice for is "Client X is declining. Should we administer oxygen/morphine/etc?" (Based on what client has ordered). We are fortunate (if you can call it that) that in our facility, our hospice patients are generally healthy, but dying. (Sounds like an oxymoron, doesn't it?)
The second most common thing we call hospice for? When we run out of hospice supplied items.