The number of possible addresses is so large that you could have every computer on the planet continuously generating addresses for as long as the universe has existed and you would still not expect to see the same address twice.

Yes, it is possible to generate the same address twice. There is nothing in the Bitcoin protocol that enforces that an address you have in your wallet is not also generated by someone else. But the numbers make it so mindbogglingly unlikely that there´s no point in worrying about it.