Keeping track of date when user profile has been updated I couldn't find a module or feature in D7 that keeps track of the date/time when a user updates their profile (any of the fields).
I'm not using profile2 and I'm not planning to switch to that, otherwise I could probably do it with the node revision.

Is there another way of doing it other than adding a "last_update" date field to the user and then using a hook_user_update() or hook_user_presave()?
I used the Rules module for this. There is a condition like "User Profile Updated" or something like this which you can use. You have then the changed and the unchanged values as tokens available for example to e-mail somebody about the changes.