If like me you have subscribed to receive regular emails from a company, organization, person, etc... (for example, I get notifications emails from Facebook, which I don't want to keep for more than a week) which you don't want/need to keep after a specific amount of days, the following Google Apps script (thanks to Sergei and Larry for giving us those great JavaScripting functionalities ;) ) will automatically do it for you.
1st go to https://www.google.com/script/start/, click on the Start scripting and past the following code.
Tips:
- Manual search in Gmail for the sender's email address to make sure that the script will find the expected emails.
- Set the delayDays variable to a fairly high amount of days.
- Run the script manually before running it automatically with a trigger.

/* Quick Gmail script to delete emails from a specific sender
older than a specified amount of days
For example, I get Facebook's notification in my inbox
but I don't want/need to keep them for more than a week.
Set the the delayDays and sender variables
Tip: to make sure the script will find the emails you want,
1st do a manual search in Gmail for the sender's email address.
If it returns the expected emails, then you're good to go.
To automatically run it, go into the "Resources" menu -> "All you triggers"
and set an "Event-Driven" "Day timer"
*/
function DeleteEmailsFromSenderOlderThanNDays() {
var delayDays = 2 // Specify the number of days before messages are deleted (moved to trash). Ex: 7
var Sender = "indoma@earthlink.net"; // specify the sender's email address. Ex: someone@somedomain.com
var maxDate = new Date();
maxDate.setDate(maxDate.getDate()-delayDays);
var threads = GmailApp.search(Sender);
for (var i = 0; i < threads.length; i++) {
if (threads[i].getLastMessageDate()<maxDate){
Utilities.sleep(1000) ;
threads[i].moveToTrash();
}
}
}