Your EMS affects the success of Sword and Hammer. Sword is your combined ship fleet that punches a hole in the Reaper armada surrounding Earth while Hammer is your ground forces that escort you to the Conduit.
Sword:
Having an EMS of less than 2500 will cause the outcome of the Sword fleet to be bad, and anything higher will result in a good outcome.
Hammer:
Having an EMS of less than 2050 will cause the outcome of Hammer squad to be bad, and anything higher will result in a good outcome. If your EMS is below 2050, the two henchmen that you bring with you on the final assault on the Conduit will die. Wanna kill Liara? That's how you do it.
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There are three endings:
Destroy the Reapers(Paragon - Red), Control the Reapers (Renegade - Blue), Merge Organics and Synthetics (Synergy - Green). There are seven outcomes: four for Destroy, two for Control, one for Merge.
The relays always 'ignite' but I'm not sure if they're always destroyed. Maybe. Basically a red/blue/green light is shown erupting from each of the mass relays as Shepard's choice is implemented across the galaxy.
The variants in the Destroy and Control refer to the state of the Earth after Shepard's choice - ranging from Earth Destroyed to Earth OK. The higher your EMS, the better.
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The big thing that's probably gonna piss a lot of people off is that when Shepard makes his choice - whatever that may be - he experiences three flashbacks of the most important people in his life. The first is always Joker, the second is Hackett and the third is Shepard's love interest.
Assuming your love interest is Ashley, Kaidan or Liara.
That's right. A lot of Talimancers are gonna be might pissed off when Liara's dumb face shows up instead of their waifu. I'm told there was a problem implementing the other LIs, so they just shipped it as is. So if you romanced Tali, Garrus, Cortez, Traynor, Miranda, Thane, Kelly or JACOB then fuck you, says Bioware.
Just so we're clear: if you romanced anyone other than the ME1 LIs, it defaults to Liara. Zoinks.
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After Shepard's choice, there's a short scene showing the fate of the Normandy and your crew. There are three variations (one of which is exclusive to the Synergy ending) of the Normandy scene:
1. Normandy Hatch: the camera will focus on the hatch of the Normandy. It will open up and nobody will come out.
2. Joker + 2: the camera will focus on the hatch and it will open up. Joker will walk out of the Normandy, along with 2 henchmen. The 2 henchmen that will come out will be the ones that the player has the highest relationship rating with. This includes Cortez/Traynor if they were romanced.
3. Edi & Joker + 2: the camera will focus on the hatch and it will open up. Joker will walk out along with EDI. They are followed by two henchmen and again, these two henchmen will be determined by whoever the player has the highest relationship rating with.  Everyone’s eyes will be glowing cause they’re now all partially synthetic. This will only fire if the Synergy option was taken.
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The "best" ending is the ultimate Paragon ending where Shepard survives. Both Control and Merge require Shepard to sacrifice himself in order to do it while the Destroy ending has Shepard being caught in a massive explosion. Shepard can survive the if you had an EMS of 4000, assuming the player alos accomplished certain criteria throughout the game. If not, you need an EMS of 5000 for Shepard to survive the Paragon ending. If Shepard survives, a short scene will fire that hints as such just before the credits roll.