The churches tend to have only birth, marriage, and death records. Governments, on the other hand, LOVE to collect data. Fortunately, as long as it's at least 75 years old or so, it should be publicly available; newer records are protected for privacy reasons. Other data to look for would be border entry records, pension records, civil service records, school records, property records, wills, tax records, and armed service records. (Click on the Vital Statistics link in the menu on the left for information relating to births, marriages and death records.
There are also organizations that require documented lineages for admission. These may be based on a common ancestor (such as the Monticello Society), on a war in which one's ancestors fought (Daughters of the American Revolution, the United Empire Loyalists' Association, and the Daughters of the Confederacy), or something about the ancestors (Mayflower Descendants).