Newspapers are an often overlooked source of genealogical information. Obituaries are obvious, but newspapers may also include birth and marriage announcements or local news related to your ancestors. If your ancestor died under tragic circumstances, it is possible that the death will be mentioned in the news section. I was having trouble finding an obituary for my 3rd great grandfather, Daniel Foster, but I did find a brief account of his death in a newspaper from a neighboring county. He was a justice of the peace and died while trying a case.
When researching immigrant ancestors, make sure to search not only English language newspapers, but the newspapers published by the ethnic community to which your ancestors belonged. You may only be able to find your ancestors in their community newspaper. Even if there was an obituary or death notice in an English-language newspapers, there may also be an additional one in a foreign-language newspaper and, most importantly, the content may be different. Different cultures may have different conventions and traditions about what is included in the death notice.
The first step is locating the newspapers. A good place to start is the website for the NEH's United States Newspaper Program, which lists the state archives which are involved in the preservation of historical newspapers. Another good resource is the Immigration History Research Center at the University of Michigan, where you can browse newspapers by ethnic group (here). Some of these newspapers may be digitized alread, but many will have to be accessed on microfilm at the archive or through interlibrary loan.
You should also check genealogical societies and organizations dedicated to particular ethnic communities. The Polish Genealogical Society of America (PGSA) has searchable indexes for death notices in Polish-language newspapers in Chicago, Baltimore and Milwaukee, which will make the task of locating these records much easier. Be careful, because the given name used will probably be the Polish form of the name, not the English form which may be used in other records. My wife's great grandfather went by the name "Walter" Szeszycki in English, but in his death notice in Dziennik Chicagoski, a Polish language daily in Chicago, he is "Władysław". It may be helpful to use other sources like the Illinois Statewide Death Index to be sure you have the right person.
The PGSA also shows how to obtain the record and provides a valuable translation guide for Polish death notices. Although it is geared specifically to the death notices in Dziennik Chicagoski, it is also useful for translating other types of Polish records relevant to your genealogical research.