My favorite Firefly episodes, plural, are Ariel and Objects in Space. I can't choose one between them.

Ariel because of Simon taking an active part in the team, because of two by two, hands of blue, because it actively advanced the story perhaps more than any episode besides the two-hour pilot, and because of Jayne's betrayal and Mal's reaction to it. I believe that Mal was ready to let Jayne die, except that Jayne begged him not to tell the others what he did; the fact that he was ashamed, I think, is the only thing that saved his life.

Objects in Space because ... man, do I really even need to explain? It's plastered with meanings, it has excellent character moments, and Jubal Early acts as a perfect foil to everyone he encounters, revealing new things about them. I loved how Simon was willing to go further to protect River than even River believed he would. I loved the oner at the end that included every character. I loved River and Kaylee having a reconciliation. I loved "That ain't a shepherd." It was a great episode.

I also really liked Serenity (the two-parter), Safe, Shindig, War Stories, Heart of Gold, Out of Gas, and the two Saffron episodes. Train Job, The Message, and the Reaver episode were my least favorite, but all still good. (EDIT: I forgot about Jaynestown. That fits into the ones I like as well.)