Its a difficult question to answer, because nothing in evolution is predestined, not even us. If the asteroid had missed, then the giant dinosaurs would have continued to dominate the earth alongside their smaller bird cousins. The Pterosaurs may have become extinct in the face of competition from birds. The Ice age would have proved tricky for the dinosaurs, but we now know that most, if not all of them were warm blooded and we also know that some had already evolved feathers, so they would evolved and adapted as the environment changed.
Its unlikely, that the mammals would have been able to diversify the way they did, if the giant dinosaurs were still around, thus is seems unlikely that humans would have evolved. This is just what I think, its a very difficult question to answer. Check out a website called 'The Speculative Dinosaur Project' and also check out a book called 'The New Dinosaurs' by Dougal Dixon; they try to answer the question.