So you've decided to play Mass Effect 3 and you've either A) Forgotten what happened in the first two games or B) Never played the first two games.
Here's a quick summary of the first two games to refresh your memory. But if you answered B, don't read this crap, go and play the games you loser!
Mass Effect - Shepard became the first human jedi, sorry, spectre, and was sent after the borg like Saren (ex-jedi) After chasing his ass all over the galaxy, you find out that the really cool ship he's been flying about in is actually a sentient robot fella called Sovereign. Who belongs to a race of robot fellas called Reapers. You made a few choices which resulted in a male or female crew member dying, shagged someone and even perhaps killed or never even met a Krogan buddy. After all that jazz you learn that the citadel, the squeaky clean deep space nine, was actually a mass effect gate, and sovereign along with the borg (geth) attacked.
You killed Darth Saren, and either saved the council or told them to go f**k themselves. In the end you all live happily ever... oh wait... ME2.
Mass Effect 2 - On a routine patrol you get horribly murdered by "The Collectors" a race that was not even mentioned or hinted about in the previous game as far as I'm aware. So the fact every race knows who they are was a bit perplexing. Anyway, your good old pal' The Illusive Man, (Charlie Sheen's dad), decides that he's got six billion dollars lying around and always wondered if he could make a six billion dollar man. So he brings you back to life and tells you to go out and kill the collectors as they're bad guys stealing humans. The game then consists of you going round the galaxy meeting up with old friends, meeting people who you wronged/helped along the way, shagging someone else and then playing everybody’s favourite batman villain Joker as he defends the ship from a collector attack. (Joker by the way is probably the most ironically named character in the game as he's the least funniest.) After this you go on a "suicide" mission (that wasn't a suicide mission if you trawled through the painful scanning for minerals on a million different planets routine)
where your team die or survive to attack a collector base. Here you get to chose who goes with who out of your allies and then you face The Terminator. A half built Reaper that looks like a metallic human skeleton (terminator). After you kick it's bony metallic ass Charlie Sheen's dad asks if you want to hand over all the technology to the sinister organisation that he works for who aren't at all space Nazis. most people told him to go f**k himself and blew the thing to kingdom come. Then Shepard decided to play Blue Oyster Cult's Don't Fear The Reaper until Mass Effect 3 came out.
I've not included any DLC in my summary because I'm a bastard. Hope this helped. :)