The following is a list of pages that describe how the handling of the initiative has changed over the ages.
As a brief history, it went from a d6 rolled by each character and monster and a possible +1 or -1 Dexterity adjustments, to a 1d6 without adjustments, to a d10 and many in AD&D 2e, to a d20 when Wizard of the Coast bought TSR and created D&D 3e.
I hope you enjoy the read as it includes many interesting gozzips gathered from all over the world wide web.
Of course, if you are playing Dungeons & Dragons version 3e, 3.5e, 4e, or 5e, you can use Turn Watcher™. It's was written for 3.5e, but it still works well for 4e and 5e. Check out the demo or get your own licensed copy on the Made to Order Software website.