The Wikipedia article on Sebaceous Glands says that they’re next to hair follicles.
From my high school biology class, I remember the teacher telling us that hair was unique to mammals.
Does this mean that mammals are the only class of animals that have sebaceous glands? Or do birds, reptiles, amphibians, or even fish have them? Or even <gasp> invertebrates?
The short answer is yes, sebaceous glands are unique to mammals.
Or no, non-mammals do not have sebaceous glands.
Take your pick.
Damn.
Then what do birds use to keep their feathers all shiny?
Most birds have a uropygial gland which produces the waxy oil they use for preening.
Great username/post match 
It depends on how you define “hair”. Certainly many non-mammalian organisms have structures which superficially and functionally resemble mammalian hair, and are also commonly (and in some cases even scientifically) referred to as hair. For example, many insects and arachnids are rather hairy, as are the leaves or stems of many plants.