I've been trying to figure that out too. I also see it as very "fluid." Leftist or socialist philosophy follows specific ideology and is easily defined, but conservativism or "the Right" seems impossible to pin down, it encompasses too much. I always want to align myself with these names since I wish to be whatever the opposite of the Left is.
I basically believe in the rights of the individual and personal liberty. That is to say I don't believe in a specific ideology since my only ideology is that there should be no "official ideology" or rules except those that insure our rights to live our lives with freedom of choice. We should be free to follow our own personal philosophies and dreams. Pretty much the opposite of socialism.
My belief is that this way of thinking comes from Anglo Saxon roots, eventually making its way into the philosophy of the English Whigs, and from there through our founding fathers into our constitution and Bill of Rights.
Tolkien, in LOTR, was writing a mythology for the Anglo Saxon era of England, the era which gave birth to this concept of freedom. I think it's clearly demonstrated in his concept of the Shire, which operated virtually without government.