Congregational churches have Calvinist roots, like the Presbyterians, but a form of church government more like the Baptists, with a high level of local church autonomy. They are strongest in New England.
As a practical matter, like most of the mainline groups, they have trended strongly liberal in recent years, but there is a wide range of current belief and practice.
Most (but not all) Congregational churches today are affiliated with the United Church of Christ, a liberal group which allows homosexual ministers.
As for the Unitarian question, here's a quote from Wikipedia:
"Despite the efforts of Calvinists to maintain the dominance of their system, the Congregationalist churches, especially in New England, gradually gave way to the influences of Arminianism, Unitarianism, and transcendentalism. "
Sorry, cut and paste: http://en.wikipedia.org/wiki/Congregational_church
And here is some of what the UCC says about itself:
"1. What does "Open and Affirming (ONA) mean?"
To say that a setting of the UCC (a local church, campus ministry etc.) is "Open and Affirming" means that it has publicly declared that "gay, lesbian, bisexual" (GLB) people (or those of all "sexual orientations") are welcome in its full life and ministry (e.g. membership, leadership, employment etc.) It bespeaks a spirit of hospitality and a willingness to live out that welcome in meaningful ways."
http://www.ucc.org/lgbt/ona.htm
I thought that doctrinally orthodox (not liberal) Congregational churches would be like Presbyterian in doctrine, but with a Baptist style of governance? In other words, Reformed Baptist but with infant baptism?