From the story of Jonah and the whale in the Bible, you might get the idea that the whale is a spiritual symbol and you're right.  The whale represents the power of the cosmic waters: rebirth and regeneration.  To be swallowed by the whale, and then escape indicates either physical death followed by a spiritual rebirth or death of a lifestyle (much like the death card in tarot) to bring about a spiritual awakening.  It is, obviously, the second that happened with Jonah.   Because the whale is a water animal that breathes air, it can also symbolize balance between two different aspects of life, physical and spiritual, work and play, etc.
    In dreams, a whale generally symbolizes a mother, or motherhood.  It can also represent intuition and awareness.  Alternatively, a business interpretation can mean that you have taken on a project that is too big for you or, if you are watching others pursue the whale, that others will have success with a project you rejected as too large for you to handle.  
    In Native American Shamanism, the whale symbolizes wisdom.  It is the eternal keeper of the records.  It has the power of song and is associated with the power of voice.  They teach us to listen to our inner voice as well as the songs of nature.
    In magic, the whale is a protector.  It opens the flow of creativity and intuition.