Add a column to existing table and uniquely number them on MS SQL Server

This will depend on the database but for SQL Server, this could be achieved as follows:

alter table Example
add NewColumn int identity(1,1)

It would help if you posted what SQL database you're using. For MySQL you probably want auto_increment:

ALTER TABLE tableName ADD id MEDIUMINT NOT NULL AUTO_INCREMENT KEY

Not sure if this applies the values retroactively though. If it doesn't you should just be able to iterate over your values with a stored procedure or in a simple program (as long as no one else is writing to the database) and set use the LAST_INSERT_ID() function to generate the id value.