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Picture, if you will, four planets sharing the exact same orbit and orbital speed, and separated by exactly same distance from each other. Each planet is the same size and roughly the same gravitational pull and are stable in this arrangement. No satellites and each has no axial tilt.
If each world's surface and atmospheric features were similar, what could cause their evolutionary paths also to become very similar?
There are two concepts at play here. Speciation and Convergent evolution.
Speciation is the evolutionary process by which new biological species arise. I won't go deep into the details as the question asks how they can be similar but suffice to say that Speciation is the explanation as to why evolution can create difference branches even in identical situations, given this, and the fact that mutation is generally randomized, there is a statistically negligible chance the the same mutation would occur upon all the planets.
Which brings us to my answer. The only way in which to ensure that evolution would be similar between the planets would be for someone to interfere with the genetic structure of the creatures on the planets. The only reason why its not impossible is because you asked for similar evolutionary paths. Can you imagine how difficult it would be to DNA sample every single insect, plant and creature on four planets to ensure they were all identical and then cull those that were not?
An alternative non-evolutionary interference would be that the creatures do not reproduce but are instead grown and released into the ecosystem at a steady rate.
But what about convergent evolution? This theory talks about the independent evolution of features, that is to say several different creatures developing the same kinds of abilities. Given our understanding of evolution (and constrained by my lesser understanding) it would be fair to say that you would still encounter inserts that appears to the casual observer to be doing similar things. Smaller lifeforms are so abundant and different that you would be hard pressed not to have something similar to ants, something similar to pollinators, etc. Plants would still be green (Assuming earth like condition, see this question.
I feel that generally you would still find the basic concepts, as survival of the fittest tends to mean that the most efficient way always wins out, so they would be common across all planets. Where you would start to encounter differences would be in the more complex life forms where you would notice changes. You would still find predators and prey, you would still find creatures that fly and creatures that swim in the seas. At this point, it all depends on how similar similar is as to if the answer is yes or no.
Since you are asking for similarity...there are only three options:
Convergent evolution
This answer here gives an excellent explanation of one way you could end up with similar life forms: https://worldbuilding.stackexchange.com/a/2496/49
You can expect that animals similar to great cats, grazing beasts, fish, monkeys and birds to evolve on any planet. They may have differences but they would have more similarities than differences. They most certainly would not be the same species or able to crossbreed though.
Cross planet transfer
Some agency is allowing animals and plants to travel from one of the planets to the other. Whether this is weird alien technology or unusual astronomical phenomena a substantial amount of life must be passing from one planet to another.
Consider just how divergent life just on two islands on earth can be and consider the divergences between different planets. Even if they all started off the same they would not remain the same!
Tampering
Some force is deliberately shaping the process. This is actually made more likely by the fact that the arrangement of four planets as described is highly unlikely to have formed by accident.
Adding a different explanations to the good existing answers:
As you have not defined how life came to exist on these four planets, I offer the idea of a common origin: maybe at some point during the genesis of this star system two big bodies collided, at least one of which contained the first proto-life form which was the basis for all life on your planets.
This event could either be the fundamental origin of the 4 planets - however it is unlikely, that any living thing would survive such an event. Alternatively it could just mean that the four planets where pelted by small meteorites which impregnated them with the first proto-life.
From there on you would have evolutionary processes as described in the other answers, but at least based upon some common proto-ancestor. This could provide some basic guidelines, which might give the four different ecospheres a bit more similarity than completely separate origins of life.
