Great news! Ancestry.com has digitized, indexed, and now has begun releasing the church records from the Swedish-American Lutheran churches. The records are from many affiliated Lutheran churches that have largely combined today as the Evangelical Lutheran Church in America. So far Ancestry.com has released records from the Evangelical Covenant Church and Evangelical Free Church of America, and it appears they may soon release the Evangelical Luther Church in America records. These records were previously available in microfilm at the Augustana College Swenson Swedish Immigration Research Center.
Records vary from church to church. They may have a history of the church, meeting minutes, membership records, or birth, marriage, and death records. Often the membership records will give the individuals place of origin in Sweden. In fact these church records may be the only place that this information is recorded here in the U.S. These records will often be in Swedish, nevertheless, they tend to be very readable and online translators are usually pretty good if you are having trouble.
It is difficult to be certain of the percentage of Swedes who were members of a church here in the U.S. but it is certainly a significant number. These are must-use records for anyone with Swedish-American ancestors.