I've got a buddy who is willing to "try" STO when it goes free to play. He tried the beta and said he didn't like it and found the ship combat too difficult to manage. This is the same friend who uses a trackball mouse. He wanted me to tell him about some of the high points of the game in terms of "quests". I explained to him some of my favorite Missions and was wondering which mission(s) will you always remember playing through?
The first time I beamed down to Defera, walked into the city, and looked up was my most memorable moment. Many social areas have been redone since then, but that was quite a nice change when it was new.
Doomsday and the Remans episodes are the most interesting now, in my opinion.
Seeing the Doomsday Machine waste that planet was pretty impressive, and despite the hammy acting Kvalk's death was a nicely inspiring lead-in to the battle. A few other things that have stuck with me after seeing them the first time:
The panorama of the city in Cutting the Cord
The "Oh ****" moment when you first see the Iconian ship and find your ship disabled
Pretty much all the shocks of What Lies Beneath - the ceiling falling on you, the flashes of hordes of Devidians hovering around you
The gates of Sto-vo-kor
Also, this one probably didn't stick with everyone, but because I went into the Devidian series blind (hadn't been watching the forums much, just heard talk in zone chat about new missions coming out), I felt kind of special that remembering details from the show tipped me off that I was about to be fighting Devidians.
What Lies Beneath definitely. Coliseum is a favorite, Cutting the Cord since I got to shoot at Sela, and Taris. The Romulan series has a lot to do with my characters' underlying storyline so it's always fun to play those.
On the Klingon side, I really like Bringing Down The House, and The House Always Wins. The Klingon side missions have a great story, and I love the arena fight in Bringing Down The House.