The main records from Sweden have an almost identical history to that of the rest of Scandinavia. Sweden officially became Lutheran in about 1527, at which time the parish priests were given the charge of keeping the vital records for the government—they were the official civil registration entity. Because of that, parish church records are some of the most important records a person can search when they are looking for ancestors in Sweden. Fortunately there are at least two good sources on the Internet that can help when it comes to your search of these records.
One of these sites is maintained by Svensk Arkivinformation (SVAR), a division of the national archives of Sweden. Their site, www.svar.ra.se, includes birth, marriage, death, census, convict, and other records. Unfortunately, many of the databases are limited as to the geographical areas they cover. The birth record holdings are mostly for the counties of Västernorrland and Jönköping. The census database, on the other hand, includes all counties in Sweden, but only the 1890 and 1900 censuses are available for all of them. A few also have the 1870 and 1880 censuses, and the 1860 census is available only for Jämtland.
Not all of the records have been digitized yet, but they are working on getting them all done. A subscription is needed to view the records on the site, but before you pay for one, you will definitely want to make sure they have records covering your area of interest.
Another site that is very good but also requires a subscription, is www.genline.com. This site has taken all of the microfilms made for the Family History Library (FHL), and put them into digital format. Genline has also included statistics that were sent into the national archives in their project. These statistics may help fill in the gap that exists in Swedish church records that were not microfilmed for the FHL from 1860 to 1895.
The records on Genline cover all the parishes of Sweden and for the time period they are available. Genline has made thousands upon thousands of digital images available, which means a trip to the Family History Library to do research in church records is unnecessary.
Each of these sites includes records not available in the other, so either or both could prove helpful in your search for lost ancestors.