For a state that can proudly include itself as one of the original thirteen colonies, it's nice to see a hearty, if somewhat scattered collection of online materials.
seven name lookup databases that generally provide a full name and place of residence, along with a pointer to offline records. There are some important African-American and Native American resources included here:
The archives also has online exhibits:
Happily, the Digital Collections of the Connecticut State Library offers a lot of additional material. Along with the usual collections of governor's papers and state publications, you'll find:
Lastly, the University of Connecticut links to a collection, The Public Records of the Colony of Connecticut, 1636-1776