The Social Security Death Index database is a handy tool for folks doing research on their ancestors or for looking up social security numbers in cases of deceased relatives where you need them in order to conduct other business. For instance I recently needed my father's number in order to facilitate a request for a police report involving his death in 1966.
I remember that the mid-90s web had this index retrievable in just one Yahoo search hit. You clicked through and were able to "search and leave" without hassle. Sadly and predictably I found trying to use it with "today's" web a bit more complicated. It seems that most sites offering themselves up as a gateway to it are trying to sell the most important last-step data to users for a buck. This would be fine except that one used to get the last-step data, the part containing social security numbers and perhaps other vital details, for free.
It turns out there are a mix of web companies doing different things with the same data in terms of commodifying it (at its heart the data itself isn't actually "free", it's re-sold by the government to these intermediate websites who then decide what to do with it), and you could go a bit bonkers searching around for a gateway site that does in fact just give you the scoop. Allow me to assist and point you straight to Family Search (.org). They offer the information straight up and in a pleasant format to boot.