Should I send a "cease-and-desist" letter to ResearchGate?
I am a law professor, and I am equally pissed with research gate.  

It would be unwise and inappropriate to give you specific advice about your own situation: this would likely constitute the unauthorized practice of law; for actual legal advice about the claims and defenses and legal strategies that apply to your situation, consult a competent lawyer admitted to the bar in your jurisdiction.  I will recount my own experiences below by way of generally informing the world what one person's approach is to one specific situation (i.e., mine).

That being said, here's how I've dealt with Research Gate.  They committed four serious affronts against me:


Fraudulently inducing me to sign up for the site by sending invitations claiming to be from my coauthors, 
Forging my name on e-mails to other people claiming that I invited them to sign up to the site 
Posting a draft of a paper of mine without permission, and 
Maintaining a profile of me on the site without permission. (This one, as others have noted, may not be illegal---I am not sure---though it is certainly offensive in context, and to the extent it involved misleading attributions of endorsement may be illegal.)


In response, after learning about 1, 2, and 4, I sent their customer service people a nastygram over e-mail demanding the forged emails stop and be unsubscribed. They sent me some useless response claiming I could unsubscribe.  I thought nothing more of it, but continued to hear of forged emails.

I then discovered 3 via a google scholar alert and really blew my stack.  So I contacted their general counsel, also listed as their contact for DMCA takedown notices and send them a DMCA takedown combined with an incredibly nasty cease and desist letter.

Their general counsel promptly replied and informed me that he'd taken down the paper referenced in #3 above.  I haven't verified that this is true, or checked on any of the other ongoing acts of wrongdoing (the serial email forgery etc).  I have some hopes that this will work, however, I am prepared to file suit against them on my own behalf should it not. 

What can others learn from my experience?  It's not clear yet.  I am of the opinion that this company operates by massive fraud and needs to be put down, but if my attempt to menace them into acting a little more law-abiding at least with respect to me succeeds, it may only be because I'm a law professor and they know that it would not be hard for me to drag them to account. 

Of the various wrongs they inflict on the world, the posting of unauthorized copies of papers is the easiest to stop---the DMCA is a blunt instrument, and, moreover, the publishers also have an incentive to put a stop to this.  The next time I see a paper of mine on their site, I may not even going to bother with doing my own DMCA, instead just turning it over to the publisher. 

The rest?  As I said, for myself personally, if the forged emails don't stop I may go looking for a class action plaintiff's lawyer, or just file seeking an injunction myself.  

But otherwise, the best choice may be prevention.  Don't sign up for their site.  Tell your friends not to sign up for their site.  Let people know if emails inviting them to do things on that site show up under their name.  Publicize their practices so that others stay away from them.  Starve the beast.