The Family History Library on West Temple Street, next to Temple Square, holds the world's largest genealogical collection: billions of records from countries all over the world, spanning centuries of births, deaths, marriages, and census data. The library is free and open to the public, regardless of religion, and the staff are trained to help visitors research their family trees.
If you have ancestors from anywhere with decent historical record-keeping — Europe, Latin America, parts of Africa and Asia — there is a reasonable chance this library holds records about them that you could not find anywhere else. Researchers come from all over the world specifically to use it.