They aren't cheap, but in some cases, copies of an SS-5 form may be just what your genealogy research needs. The form shown here is for my wife's grandmother. She listed a different father on this form than her children listed on her death certificate, obituary, and other records for which one of her children was an informant.
The SSDI at Rootsweb can be searched for free. It can also be searched on our page which has more information about the SS-5 form, including how to obtain it. I usually only obtain SS-5 forms when I have a big "brick wall" or records created after the person's death are insufficient.