Where colonies of European immigrants arrived in the United States, often as religious groups, it is also possible to find some early records. Pilgrims, Quakers, Dutch Reformed, Presbyterian, Methodist, Mennonite, and other close-knit groups have many records that can be used back into the 1700's in many cases, with a few being available into the 1600's.
To find these types of records, check with the Family History Library as well as libraries and genealogical societies in the reas you are researching. By contrast, when individuals arrived in the U.S. as single or nuclear families, not attached to any religion, very often nothing exists about them in the way of church ecords in the first and second generations, thereby creating many roadblocks to tracing their ancestry back into Europe.
There are numerous other books in print containing the church records of local congregations. Check the Family History Library and libraries and genealogical societies in the areas you are researching. For example Alfred Andrews in 1867 compiled Genealogy and Ecclesiastical History of New Britain, Connecticut. Farmington, Connecticut, founded in 1645 had by 1707 grown to the point where the Great Swamp area was granted permission to become its own ecclesiastical society and found a new church. Every communicant member of the church from 1758 to 1867 is included in this study. Thousands of such records exist and have been preserved throughout the nation.
Church records include many varieties. There are the standard baptism, marriage and burial records that most of us think of. In addition, you can often find the following:
CATHOLIC - http://www.bawue.de/~hanacek/info/darchive.htm
EVANGELIC - http://www.bawue.de/~hanacek/info/darchive.htm
JEWISH - http://www.jewishgen.cgsg.com
LUTHERAN - http://web.mit.edu/afs/athena.mit.edu/activity/l/lem/www/elca-home
MENNONITE - http://www.uwinnipeg.ca/~concord/cmbs.htm
METHODIST - http://tarzan.drew.edu/athome/html
MORMON - http://tarzan.drew.edu/athome/html
QUAKERS - http://www.innerlight.com/genepool/quakers.htm