Voyager Season 2 Essential Episodes

1- The 37's
Ok, so they LAND Voyager and Janeway meets up with Amelia Freaking Earheart. (Is it possible to know that this exists and not immediately watch it?) The crazy thing is that Amelia Earheart's appearance is not the most interesting thing about this episode. In fact, the great thing about this one is Voyager finding a whole M-Class world populated by humans--not human-looking guys with a weird turtle glued to their head--actual humans. Janeway declares that anyone who wishes can stay behind and make the planet their new home. The reveal wherein we see who chooses to stay on the planet makes for one of the best scenes in all of Star Trek: Voyager.

2- Twisted
This one is pretty much an X-Files episode. A spacial rift-thing is screwing with Voyager's makeup and the entire crew roams the (constantly shifting) corridors attempting to fix it. The great thing here is how everyone is eventually thrust together and how they each cope with their hopeless situation.

3- Tuvix
Neelix and Tuvok, by way of a crazy transporter accident, turn into one guy who integrates with the crew and gets used to life on Voyager. This is a classic episode of Voyager and it stands out as one of the most memorable stories ever told in Trek. What seems to be a silly, improbably premise quickly shifts into a story with a heart and teeth.

4- Meld
Speaking of The X-Files, remember Luther Lee Boggs? He's the psychic serial killer in what's probably my favorite episode, Far Beyond The Sea. Well, he's back in Meld and he's a completely different guy psychic serial killer named, Suder. Tuvok, who's all about logic and law, catches Suder almost immediately but can't reconcile his logic with the complete the idea of a meaningless murder. This quiet, emotional episode is well-executed from every angle.

5- Basics Part 1 & 2
Here's the Season Finale/Premier so it's actually two episodes but you really need to watch this one because Seska's back and all kinds of crazy mess happens when she shows up announcing that she's Chakotay's baby-mama.
Bonus Points for Suder's amazing guest appearance.
Extra Bonus Points for Tuvok basically revealing that Vulcans are exactly the same as Wood Elves.
Extra, Extra Bonus Points for the very Star Trek motif of Voyager's crew interacting with a primitive, hostile culture.

Runners Up:

Lifesigns:
The Doctor's first date. This is a sweet, unconventional love story with an amazing character at the helm.

Deadlock:
Two Voyagers. Two Janeways. Two B'Elannas. One Harry Kim. What more do you need to know?