TNG - "The Big Goodbye"

Picard, Data, Beverly, and a redshirt go to the holodeck in order to act out a 1940s detective story. Once there, a glitch turns off the safety protocols, making the story life-threateningly real. When a villain in the program holds the crew hostage, Picard tricks him into stepping outside the holodeck and de-materializing.

With this episode, the holodeck can now do virtually anything it wants; it's basically a window into imagination. It's also nice to see some of Picard's fun side as he dives headfirst into the role of Dixon Hill, P.I.

At the end, we actually almost come to care for the holodeck characters. They're only made of photons and bits of data, yet, when programmed properly, appear to be self-aware. What are they, exactly? Are they people? Do they truly exist? We're only left with that brief question, then returned to the ship. These kinds of "big questions" are exactly the kind that Star Trek was created to answer, and it's great to see TNG delve into them a bit.