Some customers like to be on top of everything, but others might not prefer that. Either way, an email notification for every minor update would almost certainly be too intrusive.
A better option would be to send email replies to the requester only when you need additional information from them, or have to notify them of a major status change. With all the other progressions in the ticket, you could just add a public note so customers who really want to keep in the loop can do so without overwhelming everybody else’s inbox. You can, of course, also choose to send out email notifications for notes but that wouldn't serve the same purpose.
A quick guide to allow non-invasive updates with public notes
Click any ticket from the Ticket List view or Dashboard to open the ticket.
Click Add note and set the visibility to Public.
Add your note in the text box and click Add Note.
Your customers will now be able to see this comment when they view this ticket from their support portal. You can also automatically notify your customers whenever an agent adds a comment to a ticket using Email notifications.