I do this quite a lot. In fact most of the games I play nowadays are games that I played growing up.
For instance the main game, and really only game I play currently is Pokémon Go on my phone. Obviously it's a newish game (came out in 2016) but I grew up playing Pokémon.
Games I got on Steam are Left 4 Dead 2 and Football Manager 2011 games I grew up playing.