I need to let end users specify a time range, to be stored and used internally as a starting date/time and ending date/time. The range could be minutes or it could be days.
There is no single answer, it depends on the context. For many places good text controls are enough. Of course such things can still help by supporting pasting and some increase/decrease actions. Maybe it can even do some validation for the value.
Then there are places that need something more. Calendar can be really helpful for entering dates and some kind of slider could be used for time. (Lotus Notes calendar has a slider.)
My advise is:
Think what you need. Don't put complicated widgets to a less used dialog.
If you need these nice helpful widgets, check if there are ready made in the library you are using and take some time to see how others have done these.
Always have the text controls with support for pasting.