I think they will be here for a while to be honest. Consoles need to get more storage within them before people will go fully towards digital games. The PS4 has 1TB of space at most straight out of the box. Considering how big game files are nowadays that will be gone quick if your an avid gamer with a large collection.
I can also see an end to disc based gaming as well to be honest, and especially because that's the way that the industry is actually wanting to go and in the end that will be the big difference.
If it was just a case of what people and the retailers preferred, then disc games probably would always be around, but if the giants such as Sony and Microsoft WANT to go download only, sooner or later they will get their wish whether we like it or not.
Generally speaking, disc based games are terrible for children, a group which plays a lot of games. They tend to throw them on the floor without a case where they get scratched and broke. Of course, in the days of cartridge games that wasn't much a problem. In addition, if games become built-in to the game system, then it would also be a solution. Anyhow, most children are so bad around disc based games that I never let them handle my video games unsupervised, with the exception of maybe borrowing one at a time.
By the way, perhaps older children might be able to handle disc based games, and I know most preteens can handle them.
With my PC's breaking down without warning and me losing all my "un-backed up" files every now and then, I would always prefer the disc based games, since it will be there forever, and it can't be wiped out by a malfunctioning hard drive. I've lost lots of game installers that I've downloaded over the years, so I would always prefer the disc installers to the software ones. So GameStop will always have customers if people think like me.
Well, honestly, I think disc games should go the way of the dinosaurs. They are from another time and more importantly, as I mentioned before, they aren't kid friendly. Instead, there should be something similar to the old video game cartridges. However, they should try to make them more modern and in the current style.
Anyhow, gone are the days when your kids could have mountains of games at their disposal for play, cause I said before, the games are likely to get scratched, dirty, and possibly even broken. Note, these games don't cost much, but the cost adds up and parents don't want to waste money.