There probably will be no solution to the over-saturation of games released on a weekly basis. And let's face it - unless you have no job, life, relationship, OR kids, you won't have enough time to squeeze out every ounce of gameplay from every game you keep purchasing. So what are the possible solutions to command this chaos?
Sure, there are sites like backloggery.com to let you chronicle your purchases and progress throughout each game, and there are the typical trophy/achievement systems that digitally date and mark how tolerant you are of your games. But despite all this, we gamers just get overwhelmed by "shiny and new" games every week enough to make our heads spin.
So you have X amount of games you've amassed - how will you tackle them?
Call me old-fashioned, but one tangible solution is just keeping a written list with you. And this is not the first time I've made this argument. But in addition to a list, why not set up a schedule to distribute your free time over your games?
Say you have three games you're playing concurrently. If you have 2 hours of free time a day, you can dedicated one hour to one game, and half-hour segments for the other two. Or, space out your time by dedicated 2 hours apiece to each game for 3 days a week.
Granted, there will be times when you just cannot leave a game to follow your schedule, whether it's trying to find that elusive save point, or you loaned your scheduled game to someone else. The best thing to do at these times is to exercise good judgment and self-control; mark the extra time spend, and redistribute your free time with your other games to compensate. And like any schedule set, you shouldn't overexert yourself and exceed scheduled time. That would just throw your planning out of whack.
But through careful time-management and creating a checkoff list, any game you own can and will be eventually cleared. Unless you just clock in a full 24-hour game-fest - then it's just a matter of sheer willpower.