First let me agree with Abigail-II: "Speed can also be an issue." Speed is a big part of what a database is all about.
Certainly, the relational model gives us flexibility and reuse of data, but speed can be the cost. If we were to use a table to define the "ID number" types, we move towards a more normalized form. The problem is in overextending ourselves in this way. Normalization can be taken to the extreme.
Moderation is a key them when deciding on the level and detail of normalization in a database. Many monks from other monasteries have preached the benefits of moderation. Many DBA's would include themselves in that bunch. Joins can become quite a task when every field must be validated against typing tables.
Regarding SSN's: I think we still have a while before we reach the point of needing additional or different base numbers. Regardless, I've oft wondered at things like SSNs, IP Addresses, Credit Card Numbers, etc. When adding intelligence into the code, like Credit Card Numbers, we greatly reduce the number of possible variants.
By the way... when will a pin be required for the use of my SSN?