Whether you want to get back into that game you loved in 2012 or you want to curiously tally how much you've spent on apps from Google or Apple the last few years, there are a couple of ways of listing all the apps you've installed through your account -- even if they're no one your phone or tablet.
As far as Android is concerned, head to https://play.google.com/apps on the web to reveal the list: scroll down and a Show more link should appear. From a phone or tablet, launch the Play Store app, open up the menu and choose My apps & games then All. Of course, you can reinstall any app from either the web or your devices if necessary.
For iOS, if you load up iTunes and visit the App Store on the desktop you should see a Purchased link down at the bottom -- this lists all the apps you've ever installed, paid or not. From any of your iDevices, launch the App Store then select Updates and then Purchased. Whether you're looking for something in particular or just want to browse, it's worth a trip down memory lane. You might even rediscover a gem you'd forgotten all about.