If there's one episode that absolutely stands out and will forever stand out from the first season pack of Next Generation, it's "Conspiracy." "The Big Goodbye" can keep its Dixon Hill. "Conspiracy" has possessed Starfleet officers whose grub is actually grub, and a dude's head being blown up. That last part really doesn't happen too often in Star Trek.
Playing off "Coming of Age" (and featuring several of the same characters), Picard and Riker make the journey to Earth in order to finally get to the bottom of things. In a lot of ways, this is Next Generation's best ever example of an original series episode, yet it also pushes forth the serialized nature of the franchise that began in the movies and would be best featured in Deep Space Nine. The sad part is that we never get to find out what the alien parasites are actually up to, left unresolved at the end of "Conspiracy" and never revisited.
Yet visually and conceptually it remains fascinating. The wiggly worms that appear on the back of the neck for anyone initiated into the plot (after swallowing space beetles, naturally) are memorable enough, but the grub Riker gets to fake eating s right up there as well, as is the resolution of the problem (i.e. the exploding head). Maybe it was because I was young when I first saw "Conspiracy," but it remains the grossest hour of Star Trek I have ever seen, and one of the true horror stories in franchise lore.
If you were wondering, all of this is still carefully nestled in the instincts of the first season. If you're looking for Next Generation to have suddenly changed, it doesn't here. "Conspiracy" is infinitely memorable, but it's still the series before it really got to know itself.
It's a new Star Trek classic all the same!
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Memory Alpha summary.