Discuss the following statement: Animal Farm is written as a fable that allegorically exposes the nature of totalitarian regimes.

I think that there is much truth in the statement.  There
is a great deal of evidence to support the idea that Orwell's work is an allegory. 
Given the fact that he wanted to vault specific and targeted criticism towards Stalin
and the Soviet Union, he very well could not outwardly say what he believes and
articulate his thoughts.  The only way he could accomplish being able to have his voice
heard and have his work published is through a form that can be suggested is "not of
this world."  Accordingly, the allegory form allows Orwell to compose a work that both
meets the criteria of the style as well as offer up a scathing satire at the same time. 
When we examine the definition of an allegory, we can see that Orwell's work meets this
standard:

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An allegory is a title="Figurative" href="../../topic/Figurative">figurative title="Mode" href="../../topic/Mode">mode of representation conveying a
meaning other than the literal. Allegory teaches a lesson through title="Symbolism" href="../../topic/Symbolism">symbolism. Allegory
communicates its message by means of symbolic figures, actions or symbolic
representation.

In
this light, one sees that Orwell's work does fit the standard in that the animals and
their farm are meant to symbolically represent elements where a lesson is
taught.