Of course, as multiple convergences teach us, evolution IS predictable (to some measure, to be sure). There can be at least 2 reasons:

Perhaps the discussion of a related question will provide grist for your mill; it concerns a mechanism for exploring your question.  See:

https://www.researchgate.net/post/Future_Predictor_and_Self-Accelerated_Evolution-any_thoughts

Of course, as multiple convergences teach us, evolution IS predictable (to some measure, to be sure). There can be at least 2 reasons:

Of course, some aspects of evoluction are unpredictable...with our actual cognitive/conscientive structures... for example: Who can predict exactly de ebola evolution impact in the world? How can we predict  the human evolution towards the few next centuries?...However, there are MEGATRENDS...

https://es.scribd.com/doc/242892332/Finlandia-De-los-mejores-sistemas-educatuvos-mundiales-pdf

I think that the problem of the evolution of complexity looks very different today than it did twenty years ago. The evolutionary acquisition of biological complexity was seen to be facilitated by the properties of complex dynamical systems that seemed to offer the possibility of  'ORDER FOR FREE'! 

I do not believe that 'blind' dynamical systems combined with random selection can form the basis for the evolution of the miriad of beautiful living forms that we see around us.

However, I believe that a new perspective is dawning with the understanding of the central role that is played by the ADAPTIVE properties of the particular types of wave that are implicated in biological functions and their development.

It came as a sudden realisation to me that ALL flesh is adaptive - at least to some degree. There are an untold number of physical skills that an individual may master in the course of his/her life and each and every one of them is catered for by subtle changes in our muscleature and bone structure - even down to the cellular level.

This amazing adaptive property of living structures is made possible by the intimate coupling between  adaptive waves (solitons - e.g action potentials and waves that are associated with microtubules) and the development of biological structure - see the references to alternative splicing and heart development in the paper attached.

It seems the emphasis is shifting from 'ORDER FOR FREE' to a more rational position that looks toward the relationship between the acquisition of biological complexity and the properties of a wave the robustness and persistence of which, results from the fact that it can acquire and embody information relating to its boundary conditions (environment) as part of its dynamic structure.

So, in order to address the question being posed above, it now seems crucial that we re-examine our assumptions regarding the role that 'randomness' plays in the evolutionary process. for me the question is this, 'Does evolution employ the same dynamical adaptive principles as may be witnessed in the living organism?'

Research that points toward the role that epi-genetics plays in the evolutionary process suggests the possibility that DNA is not a code as is commonly understood, but rather a character set which can be potentially used to create any phenotype.

 It seems very clear to me that it is the environment that drives evolution and the evidence of convergent evolution shows that our reductionist thinking that places DNA (via mutation and natural selection)  at the centre of the evolutionary stage may be an error.

If the environment is the real creative force behind the evolutionary process then I have no doubt that should the clock be reset and we allowed that whole process to begin again then the dominant species on this planet would be a meta-species, just like ourselves, but with a different structure of DNA. - not humanity, nor any species, is defined by DNA!

Article The Candle and the Flame:- Structure, Energy, Information an...

Thanks Christopher I was thinking the question in that way, I didn't want to ask if there are patterns in the macroevolution scale, Neither if we can make predictions to long term periods like the question of How can we predict the human evolution towards the few next centuries? (I would like start with the microevolutionary process). And I think that the current ebola's infection impact is not so unexpected as William says, see http://cmr.asm.org/content/19/3/531.full.pdf+html

I think we cannot talk about this topic, just with a few limited cases (animal cases), I think that this question needs a deeper seeing, e.g. Igor has proposed an interessting point "Laws of biological systems that define anisotropic landscape of possible biological forms (attractors) " no so discussed before in the empirical version of this debate, that could apply to microevolutionary dynamics

And Christopher has exposed a non-conventional ideas about the evolutionary dynamics, although I didn't understand completly what means "the ADAPTIVE properties of the particular types of wave(?) that are implicated in biological functions and their development".

These points are in an ontological direction, where we can discuss over the predictability of the evolutionary process , like the proper role of randomness in the Evolutionary biology

The number of ways that a living organism can move effectively in water are not infinite and are very well contrainted and so I expect more or less the same solutions that have evolved to this problem would evolve if we would rerun evolution.  The fact that sea mammal are very similar form than fishes and uses a tale like them.  Sea mammals evolved from terrestrial mammals.  Vision and eyes have evolved multiple independ times.  Against a case demonstrating that most likely vision would be part of multicellular animals if evolution was rerun.  Harvesting the light energy of the star is would be most likelypart of any evolutionary scenarios.  To have trees organized the way they are is most likely as well.  The paths to the solutions to movement, to harvesting energies would likely be different but the solutions would likely be very similar.  

To answer the question that would organisms evolved the same way they did before if the clock rewound, we have to ask whether the geological condition of the earth would change the same way first. If the geological situations change the same way as it happened during the past 4.5 billion years, then many seletion pressure would be act in the same way and the evolution would be predictable. Thus I agree with Igor on this premise.

To some extent, I agree with the statement that evolution is predictable. For one reason, although the DNA and chromosome mutation are random and seem to be unpredictable,   the similar selective pressures, like Igor's point, and the nature selection can help choose certain morphology or phenotype that adapts to the environment best, so the random mutation of DNA and chromosome are not really "random appearance" in the long-time process of evolution. However, if we plan to regenerate the process of evolution, can we create the nearly identical geological condition? if we have the identical geological condition that similar to billion years, is the selection pressure identical to all of (or most) creatures?