Gmr_Leon: some free games every month (PS Plus) or twice a month (this differs between 360 and Xbox One). You get to keep access to these games as long as you maintain your subscription, but as soon as you decide to drop it, you lose access to all those games.
That's only true for the PS. On the Xbox you get to keep the games regardless of whether you keep the sub.
As for the subject itself, I don't see game subs as different from Netflix, book libraries, etc. Some people (especially those who are the biggest content consumers) can save a lot of money by going with subs. For games, unlike other media, there are cases where a game can be played for a very very long time (due to multiplayer or mods), and in those cases a sub doesn't make sense.
In any case, subs don't signal the end of purchased games any more than other rental services spell the end of sales for those kind of products. Sure rentals can have an effect on sales, but it's not that marked.