There are a myriad of online genealogy databases and resources to consult when looking for records for ancestors, depending on the locality and topic of research. The most important and voluminous overall are the four key databases below. For additional sites and resources, visit the BYU Family History Library alphabetical list and resources list.
Saints by Sea (1840-1932) contains immigration records for Latter-day Saints coming to America.
Missionary Database (1830-1930) has missionary records and information.
Pioneer Database (1847-1868) contains information on 61,000 pioneers.
Joseph Smith Papers contains primary source documents for prominent early members.
FamilySearch is a shared family tree with numerous free genealogical resources and information.
Ancestry.com (available only on the BYU campus) is an extensive family history database that offers more than 1 billion names.
Findmypast offers more than 1.7 billion international family history records.