This is a very fast, efficient Borg deck designed around Service the Collective.

Draw Deck:
2 Interlink Drone
2 Countermeasure Drone
3 Bio-Med Drone  (There are not too many drones in this deck, so be sure to reuse the ones you have.  3 Bio-Meds together will beat Aphasia Device / Tarellian Plague Ship combos, even without an Interlink.)
Assault Drone
Astrogation Drone
Seven of Nine
4 Borg Queen  (Select Treachery to protect yourself from Unscientific Method, or Empathy to guard against Cardassian Trap.)
4 Locutus of Borg
Borg Cube
Borg Scout Vessel
3 Transwarp Network Gateway
3 Establish Gateway
3 Adapt: Negate Obstruction  (A small number of Adapts suffice, since you can get past many dilemmas by sharing the Counterpart's skills.)
5 Awaken
3 We Are the Borg
Regenerate

In the Tent:
Astrogation Drone
Cyber Drone
Guard Drone
Multiplexor Drone
Quantum Drone
Survey Drone
Transwarp Drone
Unity Drone
AU Door
Establish Gateway
Assimilate Homeworld  (4 Establish Gateways and this will overcome opposing Q's Planets.  It will also get you past The Big Picture.)
A Change of Plans
Altonian Brain Teaser  (Used to counteract Q's Planet bonus points.  Your metagame may vary.)

Q Flash:
2 Mandarin Bailiff
2 Penalty Box
Fightin' Words
Hide + Seek
I Tried to Warn You

Missions:
Investigate Rogue Comet
Explore Dyson Sphere
Repair Mission
Tarchannen Study  (Yes, you can only use one objective on this mission now.  You'll notice the deck doesn't have Assimilate Planets in it anyway.  They tend to be difficult to scout and probe for.)
Espionage Mission
First Contact  (Usually, having one mission you can't assimilate will fool the opponent into thinking you're not playing Borg.  Tarchannen helped with this, too.)

There are 2 criteria for selecting missions for this deck: low span and protected by Fair Play.
 

Dilemmas:
Unscientific Method - No Loose Ends - Hippocratic Oath - Scientific Method
Q Flash - Borg Servo - Friendly Fire
Edo Probe - Q Flash - Friendly Fire
Borg Servo - Q Flash - Berserk Changeling
Q Flash - Borg Servo - Dead End
Lack of Preparation - Edo Probe - The Higher the Fewer - Dead End

The dilemmas are designed to slow down / annoy the opponent.  Filter out their personnel, kill a few, reduce their skills.  By the time they can get enough people for missions, you will have completed your objectives.
 

Other seeds:
Borg Outpost
Spacedoor
Complink Drone
Transwarp Network Gateway
Fair Play
Establish Gateway
Service the Collective
Q's Tent
Q Flash
 
 

Strategy:  Well, I planned out this deck the morning of the latest Current Rulings planning on basing it around 4 objectives on the 2 dual icons. When that got shut out that night, I revised it to focus on purely busting through dilemmas with Borg adaptability at 4 space missions as quickly as I could, with Service to speed things up.  The basic plan here is to draw until you've got a Queen and Locutus in play (shouldn't take very long), then book it to the Alpha Quadrant and start establishing gateways at your space missions (Or your opponent's, if you'd like.  The dilemmas can easily be mixed up to make it easy for your Borg to get by, especially if your opponent is not using Q-flash.  This could be sketchy now with Q the Ref, but there's one extra Establish Gateway to lose to Access Denied.).  With the awakens/Queen downloads, I always get Seven first, followed by the Assault Drone (the only, and one of the only bad probes), then at least one Bio-Med (to be supplemented with at least 1 more after you've got a good selection of drones already), then an Interlink.  Once the Queen/Locutus are out, I never draw from the deck anymore, just download.  Once you've got a good probe on top, you can download from the tent to keep from changing the probe.  Locutus' Officer, Diplomacy, and Leadership work great for getting you by Shakas, Friendly Fires, Maglocks and the like, while keeping the Queen with Treachery keeps the collective safe from Unscientific Method (I see these dilemmas a lot).  The only space dilemma that really tripped me up was Orion Syndicate Bomb (Didn't expect to see it, never bothered getting the transporter skill drone.  Got hit by this one 2 games in a row…..).  I think I only had to adapt to about 3 dilemmas total during the entire 4 round tournament, and those were mostly planet dilemmas at Tarchannen Study.  It might be better to find a straight space mission to replace this one, I was just in quick need of a low-span space Federation mission.  If for some reason you start going through your deck too quickly, you can slow yourself down by using one draw to download a drone to your hand, and another draw to download the drone into play.  All of this, of course, is from pre-TwT, I'm sure there will be some interesting new changes in the next few weeks.
 
 
 
But I don't own 4 Locuti!
Deck design variations by Chris Brennan (aka Rom)

    For a Cardassian version of this deck, use 4 Dukat of Borg.  Of the 4 EFC counterparts, his skills are closest to Locutus.  You really need to use a counterpart with Officer to help with Maglock and Hazardous Duty.  Dukat has Treachery already, so the Queen should always have Empathy.  You'll need a seeded Spacetime Portal in place of a dilemma.  (Hippocratic Oath might be the least important dilemma there.  Or simply create a new 3-card combo in place of the Science combo.)  You might want another AU Door in the deck to help keep the STP open, just download that bad probe to your hand when you get a chance.  Use the following missions: Orb Negotiations, Intercept Maquis, Intercept Renegade, Protect Shipment, Verify Evidence, and Search for Survivors.  Yes, there are other Cardassian Icon space missions, but these look like they belong together in a Cardassian Gul deck.  A Characterize Neutrino Emissions would look out of place, possibly hinting at a Borg deck.  Search for Survivors is just a bluff, like First Contact.
    It would also be possible to build a variation with 2 Dukat of Borg and 2 Bariel of Borg, using the 2 homeworlds as your 2 planet missions.  That gives you some flexibility with skills, and threatens 2 different affiliations with Assimilate Homeworld.
    If you don't have 4 Queens, substitute 1 or 2 more Adapts for each missing Queen.