There are so many! "This Side of Paradise", in which Spock falls in love and is reduced to tears. is a favorite of the original. Of course, the Khan episode and resulting flick #2 "Wrath of Khan", can be watched over and over ........ TNG would have to be my favorite spin-off series, with DS-9 and Voyageur next. I just watched episodes 1&2 of DS-9, and enjoying watching the series again! It's been a long time. :D
It's hard to say fav episodes of any of the ST shows, indeed, the original had "Trouble with Tribbles" ,,,, Spock's arranged marriage episode "Live Long and Prosper" what a great one that was, and Captain "Jerk" had so many women - even a green one! :P Too many to choose just 'one'.
tal