Do you know who I am? 2(requires some specific movie and book knowledge)

Am I a man? Am I a puppet?

I am neither, for I have shuffled off this mortal coil,

And indeed have no strings to hold me down.

My family is many, yet I worry not for them.

Some are strongly with my cause, and others completely against.

My cousins include Jarvis and HIVEmind,

My brothers Overlord and Skynet.

I am much like my brothers,

Since I need not keep to a single weak vessel.

My eyes are the color of the moon's home,

Where sleeping dragons should not be woken(nor tickled).

And watch out, for I am coming

To rid the world of your doomed existence.

I would go with:

Ultron

BEWARE:

watch out for ultra spoilers from Avengers: Age of Ultron

Am I a man? Am I a puppet?
I am neither, for I have shuffled off this mortal coil,


He is quite aware of what he is.

And indeed have no strings to hold me down.


Reference to the trailer "but now I'm free, there are not strings on me"

My family is many, yet I worry not for them.
Some are strongly with my cause, and others completely against.
My cousins include Jarvis and HIVEmind,
My brothers Overlord and Skynet.


AI is the family. In books & movies many AIs want world domination. However, many also want only to help humanity. "Brothers" are those AIs who want to end humanity. "Cousins" are those that help it.

I am much like my brothers,
Since I need not keep to a single weak vessel.


Since AIs are digital (more or less) they do not have only one body. They can easily migrate to another one or occupy many at once.

My eyes are the color of the moon,


In the Avengers: Age of Ultron movie, his eyes go from a yellow-ish, moon-ish color to red. Depending on atmospheric conditions the moon can have a red-ish color. Alternatively Ultron is created through the mindstone (which is Yellow).

Where sleeping dragons should not be woken.


Ultron was "awoken" by Tony Stark.

And watch out, for I am coming
To rid the world of your doomed existence.


Ultimately Ultron wants to kill of humanity to achieve peace.

• The eye color part isn't right, though it does fit... I meant his eyes at the very beginning. – AJL May 11 '15 at 11:18
• Edited the line a bit to make it somewhat clearer. – AJL May 11 '15 at 11:30
• @AJL I see, I'm not familiar with the Harry Potter Universe. For me, the no-strings part was the one that ultimately gave it away. – dmg May 11 '15 at 13:40
• Yeah, there's usually one thing in riddles like that. My crude ones at least. – AJL May 11 '15 at 20:01
• @AJL Nah, pretty much all of them have that one "a-haaaa" line in them. – dmg May 12 '15 at 6:47

The Terminator

Seems a bit too easy, especially given

Skynet

which I think everyone would recognise.

• I think you answered a bit too soon. It doesn't exactly fit the whole thing. – AJL May 11 '15 at 11:19

I think that dmg is right for the most part, except I think that the last two penultimate lines,

"My eyes are the color of the moon's home,

Where sleeping dragons should not be woken."

Actually should be interpreted to mean the color blue. When I think of Sleeping dragons, I think of The Hogwarts school motto, "Draco Dormiens Nunquam Titillandus," or, "Never tickle a sleeping dragon." The moon would symbolize Luna Lovegood, and I think the "moon's home" refers to Ravenclaw house, who's color is blue.

• +1 For getting it, but ultimately, I think dmg had it right faster. – AJL May 11 '15 at 11:40