If your chain is severely stretched, you will notice one of two things:

A. Your chainring teeth will have indented at the pusher edge (the teeth will look like a shark fin)
B. Assuming the chainring has not given into the chain's wear, the chain will ride UP on the chainring, exposing gaps under the chain, when on the chainring.

Less noticeable - by eye - is wear on the freewheel cogs. It is almost impossible to accurately gauge a freewheel's wear in this manner. However, it is quite easy to know if it is with a new chain - a worn freewheel causes the chain to skip on the cog with the most wear; often the lowest cog, if the previous rider was shifter-shy.

-Kurt