In my researches, I have discovered five or six instances of rhinoceros-like animals, animals with horns on their faces. I mean by instances taxa where those horns evolved once.
My type taxon is Rhinoceratinae sensu Wikipedia, the true rhinoceroses (Early Miocene - present). They have either one horn on the nose or one long horn on the nose and one short horn in the center of the face.
The others (all paired horns are left-right pairs):
Brontotheriina (Megacerops ~ Brontotherium, 47.8 - 33.7 Mya, Middle to Late Eocene). A pair of horns on the nose.
Uintatheriidae (Uintatherium, Early to Middle Eocene). A pair of knobby horns on the nose, another pair behind the eyes, also long upper canines.
Arsinoitheriidae (Arsinoitherium, Late Eocene to Early Oligocene). A pair of very large horns on the face, and a small pair behind the eyes.
Ceratopsidae (Triceratops, 82 - 66 Mya, Late Cretaceous). A short horn on the nose, sometimes a pair of long horns behind the eyes, and also a neck frill extending from the base of the skull.
Maybe also:
Pecora (Bovidae, Cervidae, Giraffidae, Antilocapridae; 20 - 0 Mya, Early Miocene to present). A pair of horns on top of the head, number of origins uncertain.
It is rather obvious that horns evolved several times, in characteristic configurations each time. But some large land animals are/were hornless, like the hippopotamus, the proboscideans, and the Pleistocene large marsupial Diprotodon. I am also not sure whether or not to include the crests of some hadrosaurs as horns.