The State Archives has an extensive genealogical research section, which includes several statewide death indexes, spanning a period of almost two centuries -- from 1763 to 1950.
Another resource at the Archives is the Chicago Police Department Homicide Record for the period 1870 to 1930, as well as a number of will and probate records, and county death certificate registers.
For example, Adams county has its own regional obituary search engine.
Local resources also include lists of deaths, which, although they don't provide a lot of details, contain one of the most important pieces of information needed for an obituary search -- the date of death.
The genealogical resources list at Death Indexes also includes cemetery records, newspaper obituary archives, and county wills indexes.
When you search for a title, the database will give you its name, period of circulation and where it was found, as well as the format of the record.
At county level, there is a perhaps surprising amount of information available via search engines and document collections.
A lot of these, all issued 50 years ago or more, are publicly available.
There is now even an online database of death certificates issued between 19.