Well, if we're going to accept that it was murder, my money would be on Cecil being the one who got the job done. He had to have known how disastrous it would be to have a Dudley on, or so close to the throne of England. Not to mention that day by day, Dudley was gaining more influence with the queen. If Amy had been permitted to die of natural causes, then Dudley COULD have possibly been an acceptable suitor. However, with Dudley 'infamed' by her death (as it were), he was completely and irrevocably removed from the list of possible consorts for Elizabeth. Let's face it; Cecil was DEFINITELY cold blooded enough to arrange the death of an innocent woman, especially a woman reputedly in deep despair over her husband's abandonment. And if that death would not only guarantee that Dudley could NEVER marry the queen, but also that he would be suspected by the people of England and lose favour in the court, well then, why not?
Personally, I find the fact that Elizabeth told the Spanish ambassador that Amy was either dead or very near so just DAYS prior to the actual murder (or suicide, or accident) to be highly suspicious. Who is to say that Cecil didn't whisper this rumour to her, knowing her well enough to assume that she would pass the tidbit on to at least one other courtier? Not to say that Elizabeth herself wasn't aware of the plan; she may very well have been if she truly had such a fear of marriage. By making it 'impossible' for her to marry Dudley in such a roundabout way, she could still keep him without being bound to him.
Just a theory, and one that has been thrown around MANY times, I know. But that's what I think.