Believe it or not, physical stock certificates aren't common these days, and we don't even issue them to customers anymore. Nowadays, securities get issued in "book-entry" form (where client ownership is recorded electronically, without paper certificates).
However (you knew there was a however coming), some securities are eligible for a Direct Registration System (DRS) transfer. This is where you send a stock to the company's transfer agent, and then the transfer agent issues you a stock certificate. For more information, please see the following: