I never really had any religious belief, in spite of the coercive indoctrination I endured as a youth. I don't have it in me to believe. Some time ago, I gave up all pretense, i.e. the desire to 'believe in belief' as it were.
If you are referring to a simple choice to attend a different denomination within Christendom, one with relatively similar doctrines to your own, perhaps (say) to smooth out a marriage, I would say it is probably quite common. It seems to me when speaking of denominations there is a core set of beliefs, more or less shared by all, and then there are all the denomination-specific add-ons that distinguish one from another; so adaptation is probably not a huge problem.
(I realize I'm oversimplifying, as there may be any number of other reasons to change which don't involve a crisis of faith. I also acknowledge that there may be a gulf of differences even between certain sects in Christendom.)
Concerning a conversion from one major religion to another: I find the notion profoundly disturbing. How can you believe one thing today and something else tomorrow? Except in the case of coercion a.k.a. 'forced conversion', I can think of no justification for such a thing. To do so suggests a weakness of faith to start with.