The Missouri State Archives has put online its index of deaths from 1910 to 1960 and has recently completed the process of digitizing the death certificates into pdf. Certificates asked for parents' names, birth date, and birth place, and most ask for the spouse. This is a fantastic source of information on 19th and 20th century Missourians.
Records are available once they are 50 years old, so a new year of certificates (e.g. 1957) is released each year (e.g. early 2008).
Pre-1910 records are spottier, but there is also an index to those on the same website.