The Nebraska State Historical Society has over 20,000 microfilms of Nebraska newspapers. You can purchase copies of most of these microfilms from the society. Many of the newspapers have been indexed in the Newspaper and Information Index available at the society, and online at http://www.nebraskahistory.org. You can get a list of the indexed newspapers by writing to the society and asking for Reference Leaflet No. 4, Newspaper Indexes. Other helpful statewide indexes to birth, marriage, and death notices are:
Nebraska Newspaper Abstracts: A Computer Index to Names and Events Abstracted from Selected Nebraska Newspapers. Alliance, Nebraska: Nebraska State Genealogical Society, 1983—. (Family History Library book 978.2 B32n.) This series now has birth, marriage and other information through 1919.
Sittler, Melvin. Sittler Index of Surnames for Which Information Has Been Abstracted from the [Lincoln] Nebraska State Journal, May 1873-December 31, 1899. Five Volumes. Lincoln, Nebraska: The Lincoln-Lancaster County Genealogical Society, 1983-84. (Family History Library book 978.2293 D22si; Volumes 1-4 on fiche 6093604-7, Volume 5 on fiche 6117319.) Volume 5 has abstracts for 1900.
A guide to help you locate Nebraska newspapers is Anne P. Diffendal, A Guide to the Newspaper Collection of the State Archives, Nebraska State Historical Society (Lincoln, Nebraska: Nebraska State Historical Society, 1977; Family History Library film 1036134 item 7).
The Family History Library collects indexes and transcripts of newspaper records and obituaries but does not have copies of Nebraska newspapers.