Socialism is:

1. An economic system characterized by worker ownership and management of the means of production.
   The labor-oriented definition, originally used by 19th century socialists, but also used today by libertarian socialists and left libertarians.
   
   
   
2. an economic system characterized by collective (cooperative, communal, social) ownership of the means of production.
   The economic definition, aka the descriptive definition, a technical operational definition.
   
   
   
3. an economic system characterized by state control, management, and regulation of the economy.
   The conservative definition, frequently used by statist capitalists and Austrian economists. What they mean is statism.
   
   
   

4. a stage of society in Marxist theory transitional between capitalism and communism and distinguished by unequal distribution of goods and pay according to work done
   The Marxist definition, a specialized definition.
   
   
   
5. a system of society or group living in which there is no private property
   The communist definition, often used by anarcho-communists.
   
   
   
6. any philosophy that gives a normative critique of the existing political or economic order.
   The original definition used by e.g. Pierre Proudhon and early critics of industrializaton.
   
   
   

7. the economic system currently existent in the Europe, Canada, and other countries - including, perhaps, the US.
   The naive definition; such economies are more accurately called a mixed economy.
   
   
   
8. the economic systems which have existed or currently do exist in the USSR, Communist China, Cuba, North Korea, Venezuela, etc.
   The nominal definition, referring to those countries which which declare as socialist.
   
   
   
9. an economic system characterized by redistribution and equalization of wealth, usually through taxation and spending in the form of social programs and welfare.
   The vulgar definition, frequently used by the “mainstream” referring to statist socialism but not libertarian socialism.
   
   
   
10. the economic belief that "labor is the true measure of price."
    The cost-price definition. Benjamin Tucker quote from State Socialism and Anarchism (1886)
    
    
    

Compare with the definitions of capitalism.

Thanks to Jeremy Brown for starting this list.