Some of the key cards for the Borg:
First, one thing to remember about Borg: they like their downloads. This is rather limited by the restrictions around downloads (either from
General Quarters or its corresponding rule in OTF), but still very important. Generally, Borg download in place of drawing cards; in fact,
Seven of Nine will let you draw a card instead of your normal card play.
A Change of Plans -- the main card that lets you swap out your
Objective.
Borg Queen -- downloads that card, or any drone, in place of a card draw. Also gives the Borg access to skills they wouldn't otherwise have.
Borg Queen -- replaces your card play, rather than a draw, but can download any
Event or Interrupt (including, of course, A Change of Plans).
Borg Queen -- gets
We Are the Borg, first to download some drones, and second to get additional draws (or free reports). Also has some regular skills so you don't need to use her skill-selection skill on those.
Nine of Eleven -- skill-sharing, including whatever the Queen has selected.
Adapt: Negate Obstruction -- gets your Borg past almost any dilemma.
Service the Collective -- lets you probe on the same turn that you finish scouting. Often used in conjunction with
Locutus of Borg and a mission selection involving
Espionage Mission (make sure you use that one, and not
Research Devastating Attack, because only the former is the Federation homeworld) and a bunch of
missions--which can also make your opponent think you're playing Federation rather than Borg. (You could also use
Data of Borg if you prefer.)
They Will Be Coming -- get a big, nasty Borg Cube barreling down the spaceline, reporting drones for free every turn.
All that said, I'm no expert on Borg, and there are undoubtedly plenty of cards I've missed.
One more thing to note: while Borg are limited to one
Objective, they can have as many
Incidents as they want. (I think that's one reason the Incident card type was introduced in the first place.)