Yes, all the time. Most insurance companies prefer generics, as they are much cheaper. Our insurance coverage, for example, charges no deductible if we use a generic version.
Other insurance policies insist a generic be used if available.
Those on tight incomes have found generics to be a life saver, as compared to prices of non-generic medications.
I have never felt a generic drug was not as good as a name brand drug, but others would disagree and so will not use generic drugs. I use generics when ever possible.
Once in a while a doctor will even state, "no substitutes" so that a generic version is not filled by the pharmacy.
So generics are used, although as with everything else, there are exceptions.