From what I've read, it was rhotic (r was hard, like in American english)... out of the very many different English language dialect variants (from Irish, to Australian, to American, etc), do we have any idea what they sounded like, and if so, what current accent they'd be closest to?
One of the world leading experts in this area is David Crystal... He's written a lot on it...
Here's a video of Crystal reading Shakespeare in an the original accents from 1600, when the British first started colonisation - http://www.youtube.com/watch?v=gPlpphT7n9s - and contains some other interesting notes on accents and the time.
*edit: I can't seem to find the article I was thinking of, but he's certainly done a fair bit of research on early American accents, one of which concludes that many of the current American accents - particularly down south - are closer to what the accents of the 1770s sounded like than English accents today...