I was rewatching a few of the Original Series episodes and it all feels just a little dated (although to be fair these were third-season episodes which are generally a bit worse). Balance of Terror is a pretty good one; I liked "The City on the Edge of Forever" a lot, but I think my favourite is probably "Mirror, Mirror". Great idea, and spawned a whole set of similar stories (mainly in DS9, with one -- sort of -- in Voyager I think).
From TNG, anything post-season 2 is usually worth watching, but a couple of my favourites would be (one from each season 3-7) "The Ensigns of Command" (Data trying to evacuate a group of colonists -- my favourite moment is Picard dusting the bridge while he's deliberately annoying the baddies); "Clues"; "The Inner Light" -- possibly the best idea in the whole franchise, portrayed to Borg-like perfection; "Relics", just for the nostalgia trip; and "Attached" from season 7. All great fun, and so are many of the rest for that matter.
I got into DS9 as a child but it sort of drifted and I can't say I remember most of the episodes. Also the War story arc dragged a bit; but perhaps I'll get back into them at some point.
Voyager I love, particularly Seven of Nine, who has an amazing set of ...character traits. (Yes, I totally meant that...). Possibly my favourite episode there might be the two-parter "The Killing Game", which is perhaps not a totally original plot idea, but still great fun I think.