Stephen Jay Gould (among many others) used to claim that life's history has been highly contingent on unlikely events. These events were so unique that they couldn't be predicted to happen -- they just did. The implication is that if the history of life were run again from the beginning, the end result would turn out completely different.
Now certainly at some level that must be true. The fact that any particular species ends up the way it is depends on the concordance of so many independent events that it just couldn't turn out the same way twice. Not to mention that many of those independent events are rare mutations that might easily failed to happen, or if they did happen, might easily have been eliminated by drift instead of becoming adaptive subsitutions. From this perspective, the appearance of any one species is due to the combined probability of many extremely rare events. Multiply all those tiny probabilities by each other, and you get the probability that life would have turned out the way it has.
But some people have argued that there are aspects of the history of life that have a good chance of happening on any Earthlike planet. After all, some important things have evolved independently many times, like flight. Large-scale generalizations like Cope's rule that supposedly apply across many different phyla hint that there may be common factors affecting the evolution of very divergent body plans and ecological adaptations. Put these things together, and you get the impression that a new instance of life on another planet like ours might evolve in broadly similar ways, even if the specifics would certainly be very different.
Possibly the most important question of this kind is whether intelligence would be likely or unlikely to evolve on suitable life-bearing planets. This "historical contingency" issue has been a prominent part of discussions about "Drake's equation", which gives a back-of-the-envelope list of factors important to the chance we will find intelligent life elsewhere in the galaxy.
Now, this paper by Geerat Vermeij addresses the question with evidence.
Many events in the history of life are thought to be singular, that is, without parallels, analogs, or homologs in time and space. These claims imply that history is profoundly contingent in that independent origins of life in the universe will spawn radically different histories. If, however, most innovations arose more than once on Earth, histories would be predictable and replicable at the scale of functional roles and directions of adaptive change. Times of origin of 23 purportedly unique evolutionary innovations are significantly more ancient than the times of first instantiation of 55 innovations that evolved more than once, implying that the early phases of life's history were less replicable than later phases or that the appearance of singularity results from information loss through time. Indirect support for information loss comes from the distribution of sizes of clades in which the same minor, geologically recent innovation has arisen multiple times. For three repeated molluscan innovations, 28-71% of instantiations are represented by clades of five or fewer species. Such small clades would be undetectable in the early history of life. Purportedly unique innovations either arose from the union and integration of previously independent components or belong to classes of functionally similar innovations. Claims of singularity are therefore not well supported by the available evidence. Details of initial conditions, evolutionary pathways, phenotypes, and timing are contingent, but important ecological, functional, and directional aspects of the history of life are replicable and predictable.
Those early-to-evolve unique things might for the most part be events that foreclose later development of the same things, by the way.
My intuition about this problem has been that some things -- if not inevitable -- were at least pretty likely. I don't think the hominid lineage is that exceptional; I expect that we just happen to be the first ones to have gotten here. There is a limit to the extent that intuition can be quantified, but studies like this one block out the possibilities.
Vermeij GJ. 2006. Historical contingency and the purported uniqueness of evolutionary innovations. Proc Nat Acad Sci USA Abstract