Definition of "free will" is the ability to act free of the will of god. What do you mean by "free will"?
UPDATE: A brief summary of compatibalism: http://www.rep.routledge.com/article/V014SECT1
According to them dogs do not have free will but people do. Probably talking about ethics and moral side of "free will" question, not physical or religious. But even there "free will" is just an illusion in your mind.
This is a philosophical question, and as such, can't really be answered experimentally. At the risk of sounding sophistical and clintonian, it depends on what you mean by "'really' free". You can be controlled by environmental factors and still exercise free will by some definitions of that term.