Keeping an eye on chain wear.

First of all, chains don't 'stretch' at all, they wear. As the internal parts of the chain wear with use they cause each link to effectively loosen. If you add all this extra movement of the links together, the chain effectively becomes longer. This is bad because when a chain is new, the pitch between each link  matches the pitch of the teeth on the chain rings and rear cogs and the pedalling load is spread evenly along all the teeth.

When the chain elongates, the chain is only effectively pulled by one tooth on the chain ring and only pulls on one tooth on the cassette. Because the ratio between the chain ring and rear cog varies depending on which gear combination you're in, this causes random teeth to wear out more than other teeth. The upshot is, you end up with dangerous chain slip that even a new chain won't fix.

It is widely said that the most wear you want to allow before replacing a chain is about 0.75%. The traditional way of measuring this used to be measuring the distance between 12 adjacent links with a ruler and bin the chain if it exceeded 12 1/16". Nowadays however it's far easier to buy a chain tool like the Park one shown in the pic and check your chain regularly.

I tend to get around 1,000 miles out of a SRAM PC971 the use of which I'd describe as road based but covered in mud occasionally but I've read of roadies who say they get 3 to 4,000 miles out of a chain.

I guess it all depends on the brand of chain, the preferred lube regime and the usage in the end!