Chain stretch is an ugly beast. Caught late, it can spell disaster for an entire drivetrain through premature wear. Besides keeping things clean and lubed, regularly checking and replacing your chain is the best thing to you can do to protect your drivetrain investment.
Bicycle chains are ½ inch pitch, meaning that there is ½ inch between each pin. Using a ruler, you can measure 12 complete links of chain, pin to pin, to determine if the chain should be replaced. On a new chain this measurement should be exactly 12 inches. A chain that measures 12 1/16 inch should be replaced before any drivetrain damage is incurred. Past the 12 1/8 inch mark and you should expect at least the most used chainring and cog(s) to need replaced for a new chain to work properly, and most likely the entire drivetrain is past its prime.
It is truly a misnomer to say that chains “stretch” as they do not increase in length due to physical stretching of the links but due to wear on the chain pins themselves. Whatever the mechanism, a stretched or worn chain is bad news all around. Inspect and replace your chain when indicated, it’s a small investment as compared to the rest of the drivetrain.