Do we have free will?

What do you think about Romans 9:18? "Therefore God has mercy on whom he wants to have mercy, and he hardens whom he wants to harden."
As I read this verse, I wondered how free will could come into play when God can harden whomever he wants, or have mercy on whomever he wants.  It doesn't seem like a situation where we could ever choose to follow God.  But Jesus himself said "No one can come to me unless the Father who sent me draws him" (John 6:44).  However, perhaps God is calling all of us to him, drawing all of us to him, and not all of us are responding.  This would make sense because, as 2 Peter 3:9 states, God "is patient with you, not wanting anyone to perish, but everyone to come to repentance."
Does Romans 9:18 then mean that God hardens those who have already decided to ignore him?  In what other way could God harden someone and still allow them to have made a choice?