They are really little more than a field. There are a couple of built-in reports that refer to them, but not a lot (unlike versions, components, status and so-on which are heavily used all over the place).
Most people who do use them end up generating their own reports and scripts - it's very common to see filters like "my issues with due date in the next week" or "my project's issues which have gone past their due date", and of course, subscriptions, gadgets (the calendar is rather handy with due date), and so-on. It's also one of the most common ways I've modified the "jelly escalation" scripts for - to automatically poke people about issues with looming due dates.
If you have a use for due dates, use them. If you don't, then skip them.
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