Excluding episodes of my own series, which I think is only fair... I'm going to have to go with Section 31 Files, "The Sum of One's Memories." I haven't listened to it in years, and can only hope it would hold up if I listened today, but I remember it distinctly for daring to explore the Big Questions Trek needs to ask -- and at a time (2005!) when few if any fan productions were even trying to do that yet. That episode, more than any other single event, turned me on to the power of audio drama. I wasn't scrutinizing the green screens or marveling at the production values (or, as was more common in 2005, the lack thereof); the story was able to suck me in with a handful of really powerful, distinct voice actors (Karl Puder, Elie Hirschman, Mark Kalita, Kara Dennison -- a top-notch cast even by today's standards), a really clean soundscape, and an intriguing premise backed up by what I remember as a solid script. P.S. Just looked it up... apparently Nick Cook was in that one, too! I'd quite forgotten. But that just reinforces what I was saying about it being a top-notch cast! P.P.S. Yeah, "Lolani" was great, but everyone already said it!
For me the one that still really stands out overall in terms of execution, and having that 'original Star Trek' vibe is: Starship Exeter: The Tressaurian Intersection (Even though it took them nearly a decade to get the final act out.)
New Voyages' Kitumba. Such a masterpiece - it had everything in it I was hoping for and missing from Into Darkness.
Yeah, I should have included Aurora also. Speaking of which... [yt]https://www.youtube.com/watch?v=cMef399bW48[/yt]