It is possible to get a notification email every time an event is changed, modified or deleted in a shared calendar (it works only for shared calendars, i.e. calendars that are listed under “Other calendars” and the calendar has to be shared as "read-only" with you). To activate this feature in Google Calendar, open the calendar’s “Notifications” page (click the gear icon in the upper right corner, then “Calendar settings”, “Calendars” (tab), “Notifications” (behind the name of the shared calendar)):
By checking “New invitations”, “Changed invitations” and “Canceled invitations” in the “Email” column you can activate the notification emails.
If the calendar is not read-only
As mentioned above it works only for calendars that you do not own, i.e. that were only shared with read permission with you. Getting notifications for a calendar for which you have write permissions is only possible via a workaround: You could create a new Google account and share that calendar as read-only with that account. Turn the change notifications on in the Google Calendar of that new account and forward the notification emails from the GMail web page of that new account to your normal email address.
Recent changes in a calendar
CalenGoo’s search view contains a function "Recent changes" in the menu that allows you to see for each of your directly synced Google calendars which events were recently added or modified.