Several factors prevent convergent evolution - among them are drift and fitness landscapes with multiple peaks.
Heritage constraints involving multiple origins can also act to prevent convergence.
Convergent cultural evolution is common. It can be invoked to explain most cases of simultaneous invention. However, proven cases of convergence are not so easy to come by - since common descent of cultural forms could also be involved in most cases. To find good evidence for "real" convergent cultural evolution, the easiest thing to do is to wind the clock back to eras in which formidable geographic barriers divided some human populations. Writing, baby slings, pottery and the domestication of animals, plants and fire were all invented many times independently. These events aren't explicable in terms of social contagion / common descent of cultural forms.
One cause of cultural convergence is technological determinism - which is an impotant historical force. Technological determinism provides a modern theoretical foundation for the progressive theories of evolution championed by Herbert Spencer.
There's also cross-realm convergence. For example, the wheel was invented independently by humans and by the bacterial flagellum. Similarly, walking invented independently by humans and by the kinesin proteins.
As I have argued elsewhere all convergence can ultimately be seen as a form of relatedness.