What Actually Happened: The early European settlement of what would become New England wasn't always a tidy affair.  The Pilgrims landed first, and founded Plymouth Bay colony.  They were followed by the great Puritan migration that settled Massachusetts and Connecticut.  Dissidents from the Puritan migration set up Rhode Island.  

There were a number of small, short-lived English colonies in the area, but by 1640 things had pretty much settled down and there were five New England colonies: Massachusetts, Connecticut, Plymouth Bay, Rhode Island, and New Haven.  Plymouth Bay was in what is now southern Massachusetts while New Haven was in what is now southern Connecticut.  Both Plymouth Bay and New Haven colonies led legally precarious lives.  Colonies had legal status through their charters--basically a document through which the English crown recognized their existence and gave them certain rights as governing bodies.  Neither Plymouth Bay nor New Haven had a charter.  As a result, Massachusetts eventually swallowed up Plymouth Bay and Connecticut eventually swallowed up  New Haven. 

What Might Have Happened: Both Plymouth Bay and New Haven tried to get charters after the protectorate collapsed and the English monarchy was restored.  They failed due to political missteps on their parts.  What if they had gotten their charters and had survived as independent colonies?  

Short-term results: King Phillip's war might have been postponed or avoided.  Plymouth Bay based it's tenuous legal claim to existence on a kind of protectorate over King Phillip's Wampanoag Indian tribe.  That claim was threatened when the post-restoration English crown drew up colonial boundaries that put key parts of Wampanoag territory in Rhode Island.  Plymouth Bay's attempts at reasserting their 'protectorate' over the Wampanoags was undoubtedly part of the cause of King Phillip's War.  King Phillip's war destroyed the Indian tribes of southern New England, and resulted in the death of around seven hundred English settlers of military age, along with hundreds of women and children.  It led to a twenty-year depression in New England.  The results of postponing that war are unpredictable.  Some type of Indian versus settler war in New England may well have been inevitable though.  There just wasn't room for both ways of life, and the Indians couldn't move west ahead of the settlers because the League of Iroquois was in the way. Let's tentatively call the short-term results a wash.

 Longer term results:  Assuming that the American Revolution happens approximately on schedule, it presumably starts with 15 colonies instead of 13.   I wonder if those 15 colonies would have ratified the constitution.  Rhode Island almost didn’t in our history.  Rhode Island had a history of struggling to avoid being absorbed by its larger neighbors.  Plymouth Bay and New Haven might have had similar attitudes because they would have had a similar history of struggling against larger neighbors. If they did ratify the constitution, that would have some interesting impacts on the north/south balance of power, and the balance of power between large and small states. 

What would the impact of those two additional small northern states be? An earlier civil war? A somewhat different constitution as large states recoiled from the prospect of a Senate dominated by tiny states? You could get anything from the constitutional convention breaking up in acrimony to proportional representation in the Senate, to a league of small New England states (Rhode Island, Plymouth Bay, and New Haven) still following the Articles of Confederation while the rest of the country adopted our constitution. Each of those options could lead to a very interesting world.