Estimates vary, but in terms of extinct nonavian dinosaurs, such as Tyrannosaurus rex, about 300 valid genera and roughly 700 valid species have been discovered and named. However, given that the fossil record is incomplete, in the sense that we've yet to discover fossils of many other kinds of dinosaurs that no doubt did exist, the stated numbers almost certainly do not reflect the true diversity of extinct dinosaurs.
One reason for this incompleteness of the fossil record is that rocks for some geologic time periods are not very commonly found on the surface for us to collect. For example, many more kinds of Late Cretaceous dinosaurs are known than Middle Jurassic dinosaurs because outcrops of Late Cretaceous are more numerous and more widely spread geographically than those of Middle Jurassic age.