As you may know the Mormons are deeply interested in genealogy, and many things are available to the general public thru the church. They are also moving to get many of the resources available to everyone via the Internet. One useful link is the Family Search page. At their web site you will find many useful items, including a free genealogy program, information about getting started with genealogy research, and so on. It is a very nice site, and I quite like their determination to get free public access to the U. S. Census indexes. The Search Records page might turn up some useful information on an ancestor you couldn't find using a simple Google search.
One place to access Social Security Death Records is at RootsWeb, a part of Ancestry.com (the people who think 30 bucks a month is a reasonable sum to use all their services). If you go to the Advanced Search page you will have even more options to narrow your search:
If your ancestor died between the right dates you might get lucky. In the sample above I came up empty, evidently great-grandmother Williams didn't have a Social Security benefit, or died on a date not covered. I was able to find her death certificate however on the Illinois State Archives web site. So be sure to check the web presence of the state your ancestor lived in. You might find information for relatives who were not enrolled in Social Security, died at the wrong time--I think I saw somewhere that deaths before 1962 probably won't show up on a search.
Another freebie available at RootsWeb are Mailing Lists and Message Boards. If there is a Mailing List for your family name you can search the archived lists for keywords or use the Advanced search to narrow things down a bit. You can also search the Message Boards in the same way, restrict your search to the particular family, then add a restrictive keyword, such as a first name or state. Another forum to look at is GenForum, hosted by Genealogy.com, which has a large number of family name forums, and is searchable. It too appears to be a part of the Ancestry.com genealogy empire, and therefore will tantalize you with stuff that sounds useful, but you can't access without paying.
The ProGenealogists is a place to go if you want to hire a professional genealogist, but they also have a couple of other useful things, for free. One place is their 50 Most Popular Genealogy Websites for 2009, the list has clickable links and a brief description of each site. One of the sites listed is an enormous collection of links, Cyndi's List. She currently has over a quarter of a million links to various and sundry genealogy related web locations, and has been at this herculean task for more than a decade.
As I mentioned earlier, I found the graveyard listings available for Macoupin County extremely useful. One place to see if you can find grave listings is Find A Grave. While you may not find anything pertinent to a particular ancestor, you may well find a listing of cemeteries for the area where your ancestor is buried, and once you have a cemetery name you may well find that the cemetery in question has on-line listings you can search. If you do find the cemetery at Find A Grave, they may well have a direct link to that cemetery's search page.