MySQL possibility to create global routines (stored procedures and/or functions)
There is no way to define stored procedures or stored functions (or events) that are global.  

One approach is to create a shared common schema and then qualify the calls to the functions and procedures with the name of that schema (CALL shared.the_procedure();).

This is something I do with my collection of custom date/time calculation functions (e.g., SELECT date_time.next_quarter_start_after(NOW())), and with the ever-so-handy common_schema framework, which, of course, lives in `common_schema`.

If you take that approach, you have to remember then when a routine is running, the "current" database automatically changes, and the return value of the DATABASE() function returns the name of the schema under which the routine was defined, not your session's current database.  It changes back when the routine exits, so if used in a trigger, it doesn't break anything surrounding it but you don't have a way of knowing from inside the routine what the current database was, if you needed to know.