When Joomla core is updated, no overrides in your template folder should be affected. That's why they exist.
On core Joomla items, overrides are going to only rarely conflict with Joomla core updates. When you override the Joomla core files, or any files, document document document. Commenting in the override file is CRITICAL if this is going to happen to you regularly and you admin more than one or two sites. You just won't remember what you changed!
Your code editor should have a "diff" feature, to compare the new file to the old and identify line by line what changes were made. If you've commented well, this diffing will show you exactly what was changed and if the file was affected by the update. Your only changes should be your overrides... anything else and you do have to go and re-override.
Third party overrides, however, become an issue only if the developer is not using the MVC structure correctly. If a component or module is laid out appropriately, the tmpl or view in question should not be affected by code updates.
If there is a major feature shift in that extension, you'll definitely need to document/comment and compare files.