The definition of "reflex" is an action that is not voluntary - ie, not mediated by cognition.  From [Wikipedia][1]:

> ... sensory neurons do not pass directly into the brain, but synapse
> in the spinal cord. This characteristic allows reflex actions to occur
> relatively quickly by activating spinal motor neurons without the
> delay of routing signals through the brain ...

So asking if there are any mental or cognitive reflexes is like asking if there are any behaviours that go through the brain that don't go through the brain.

The common colloquial definition of "reflex" is an automatic or involuntary action, like the way an experienced tennis player reacts to the ball without thinking.  In cognitive psychology, this is typically referred to as "[unconscious][2]" (rather than reflex).  Some authors have compared conscious to unconscious using the [iceberg metaphor][3], so if you go with this definition, then the number of mental reflexes far outweighs voluntary actions.  The entire field of [perception][4] (just as a simple example) would be included.


  [1]: https://en.wikipedia.org/wiki/Reflex_arc
  [2]: http://en.wikipedia.org/wiki/Unconscious_cognition
  [3]: http://en.wikipedia.org/wiki/Freudian_iceberg
  [4]: http://en.wikipedia.org/wiki/Perception