I still find it amazing that I can connect my Xbox 360 to the internet and play a game with someone whom I have never met, nor will I ever meet again. It still freaks me out to know that I have a library of Xbox Live Arcade games that I do not have boxes for. Without a physical library, it's hard to remember that I bought games like Castle Crashers, or Mega Man 9.
I think part of the reason that I don't consciously remember that I own digitally-owned goods is that some day, I won't own any of those games anymore.
Authentication servers get shut down. Games are de-listed from the Xbox Live Arcade. Sure, I've got the game saved on my hard drive, but what if my 360 hard drive breaks in five years? What about the stuff I have paid for?
I primarily collect older games. The main draw for my love of older games is definitely nostalgia, but there's something about the finite nature of an old game cartridge. You have a game, and you can play it forever. A copy of Super Mario World will always work on your Super Nintendo, without any extra authentication or online passes. You can still play the original Mega Man, provided that your NES can still draw power.
Ever try playing Marble Blast Ultra? Good luck. It was de-listed from the Xbox Live Arcade a few years ago. The same thing happened with Marvel: Ultimate Alliance downloadable content. Tons of Rock Band songs are getting removed due to licensing rights expiring.
To me, it really seems like game companies are not putting any focus on long-term use for their products. It's always just here and now, and that really needs to change. I'd like to look at my PS4 games 15 years from now and still be able to play Killzone: Shadow Fall without anything going wrong.
Unfortunately, I don't think that will be possible.