A few producers are some of the most powerful people in Hollywood, but most are just shlubs begging the studios for gigs. The real power goes to the movie star who puts the butts in seats.
While there may be other producers above them on a film, or a studio exec or investor to answer to when it comes to finances, most of the decisions on a film begin and end with the producer. The producer hires the director, the writer, the actors, and most of the department heads. He is their boss and does have the power (at least in theory) to fire them.
Politics muddy the waters some. They have to know who is a friend of whom. That grip they just fired may be the cousin of one of their primary investors. The lead actress may have one of the most powerful agents in Hollywood. The director may be the favorite of the studio at the moment and actually be able to get away with some of his crazy ideas on how to shoot the movie. Even with all of these complications, the producer is still the closest thing to top dog. In the entertainment industry's shark tank, the successful film producer is the Great White. (Which reminds us—we need to remember to DVR Shark Week.)