You can follow tickets that you have view access on but are not specifically assigned to by becoming a Ticket Follower. You can receive email notifications on these tickets as long as you have the appropriate notifications option turned on. To become a ticket follower, select the ticket you wish to follow and then select the Ticket Follower tab, located directly above the ticket timeline.
This will display users currently following the ticket. Simply click your cursor in the white space next to these names and either select from the drop-down list or begin typing the name of the user you wish to add as a ticket follower (including yourself).