So, I am genuinely in theory's situation - one of my friends has never seen any Star Trek and is asking me what to watch. Here's the list of episodes I would recommend, from The Next Generation:
Season 1: WATCH the following:
Encounter at Farpoint
The Last Outpost
The Battle
Hide and Q
Haven
Datalore
11001001
Coming of Age
The Arsenal of Freedom
Skin of Evil
We'll Always Have Paris
Conspiracy
The Neutral Zone
Rest of the Series: DON'T WATCH the following:
Shades of Gray (Season 2)
The Host (Season 4)
Sub Rosa (Season 7)
The first season, I am just trying to hit the good ones plus the ones which have important set-up. Probably half of those episodes I am suggesting are still rather bad. Later on, there is the odd bad episode here and there, but they're not too common. The three I list are just so, so bad, though.