Yes and no.
I would say NO, it's not necessary to play the previous games but YES, you do need to experience the story so far to get what's happening. Just go to YouTube and watch the cutscenes for each game or find a good plot synopsis video for the entire series.
The story is pretty convoluted and complex, but epically awesome. I can't imagine jumping into 3 with no prior knowledge of the story. Although 3 will likely start with a recap of the story so far, I would still recommend watching the cinematics online.
I just started Brotherhood myself, and it has been about a year or so since I played 2, so I had to watch some scenes on YouTube to bring me back up to speed. And I just pre-ordered 3 so I have some work to do over the next few weeks, but the story will be nice and fresh in my mind when I start 3.