Ever since getting into DS9, I've seen almost all of Trek. I consciously avoided some of the worst of VOY and ENT (Favorite Son, A Night in Sickbay), but those aren't major in terms of anything but disaster. 
I've seen all of TOS and DS9, all but the impossible-to-watch of VOY and ENT. The series I've seen the least of is TNG, and that's mainly just not watching the first two seasons. I've seen the major stuff like BOBW, etc.
A disaster that big is mandatory viewing. Just so you know what the screaming is about.

I've seen all of TOS and DS9, all but the impossible-to-watch of VOY and ENT. The series I've seen the least of is TNG, and that's mainly just not watching the first two seasons. I've seen the major stuff like BOBW, etc.
On the other hand, I have avoided watching These Are The Voyages. Enterprise was headed in such a great direction before its cancellation that this finale - given all that I've heard - would probably only depress me.
A disaster that big is mandatory viewing. Just so you know what the screaming is about.
