I currently don't have any games on Steam or GoG, I'm yet to embrace the download/online generation. It will happen, just not yet. I buy all my games either directly from the creator's home page (which is kinda download generation) or on actual disc, with the former becoming more the norm as shops gradually stop selling discs.
I tend to go through more discs than I keep, however, with only the ones I particularly liked staying on my shelf - and even some of those get 'lent' to friends and family. On my keepers shelf at the moment is 32 games and I have another shelf of games yet to try which accounts for 17 games and I have a handful of old big-box games in a closet that I just never got round to trading-out in one of my many clear outs and now they've developed collectibility/nostalgia. I've probably traded-out approximately 100 games over the years, but I wont have played many of them to completion.
Maybe when/if discs are fully archaic I will start buying White Elephants again to adorn my empty little shelves.