I'm assuming that all you readers out there in Internetland are scrupulously honest and would never jump a turnstile or push in behind someone on the Paris métro. But those darn little white tickets do have a way of getting lost once you get in the system.
For the most part, you don't need the ticket to get out but hang onto those suckers until you exit. Because you never know when you'll turn the corner and there will be half a dozen green blazered RATP agents ready to make sure you're completely legit. There's a hefty fine if you don't have a ticket and they'll make you pay on the spot too. They always work in teams so there's no escaping, unless you turn around and head back the way you came from. (And believe me, I've seen people doing that.)
Controls on suburban trains (whether RER or the SNCF's Transilien) seem less frequent and my guess there are plenty of freeloaders since many of these trains can be boarded without going through a turnstile first. The same goes for the so-called Grand Lignes (intercity rail service); on our late October trip to the southwest, we were four hours into a five hour ride before anyone checked our tickets. I'm sure there are folks who get a thrill from beating the man; personally I'd rather ride the rails with a clear conscience.
A contrôleuse checking tickets for passengers leaving Gare St. Lazare headed to La Defense and points west.