As in most cases you do not need your boarding pass after entering the plane, keeping them for a few days after arrival should be enough. People mention keeping them till your air miles show up on your frequent flyer account.
Other reasons to keep paper boarding passes are to keep records of your flights, to show border officials you really left the country when you say you did (in those cases where you do not get a stamp in your passport,) and as bookmarks.
The only thing of those you can not do with images or digital versions is using as a book mark.
For all the other uses, digital versions or images will do.
Only when you have left a country where you would expect a stamp in your passport and did not get one, or when you leave an area where you will never get a stamp in your passport (like the USA) you may want to keep that paper boarding pass, till you are sure your departure has been recorded (or you have follow up stamps in your passport which show you have left the country.) But if you only have a digital version, you can still show which flight you took.
Risk takers do not keep the paper versions, while the belt and braces kind of people do keep paper boarding passes for a long time.
More hints and tips in this answer.