Voyager is my favorite series, and Kathryn Janeway is my favorite captain. Just think about it: stranded in the Delta Quadrant, 70 years from anything Starfleet related, and she makes the decision to keep on truckin'. She could have decided to colonize the first suitable M-Class planet they came upon, but her desire to get not just herself, but the entire crew home supersedes this.
As for episodes, I think Janeway is reperesented the best in "Year of Hell."
Here's proof:
Janeway: "Tuvok, I can hear your objections already. I am not leaving."
Tuvok: "Given Voyager's damaged state, the probability of your surviving an armed conflict … is marginal."
Janeway: "Oh, I know the odds. But I have to stay. Voyager's done too much for us."
Tuvok: "Curious. I have never understood the Human compulsion to emotionally bond with inanimate objects. This vessel has done nothing. It is an assemblage of bulkheads, conduits, tritanium – nothing more."
Janeway: "Oh, you're wrong. It's much more than that. This ship has been our home. It's kept us together. It's been part of our family. As illogical as this might sound, I feel as close to Voyager as I do to any other member of my crew. It's carried us, Tuvok. Even nurtured us. And right now, it needs one of us."
Tuvok: "I respect your decision. Live long and prosper, Captain."
Janeway: "Same to you, … old friend."