By the the time you have shifting or skipping issues due to a worn chain, you'll be in for replacing more than just the chain. In fact, if you replace just the chain at that time, the issues will most often get worse!
Then again, the first issue some cyclists notice is the chain breaking. This can cause a serious injury if it happens at the wrong time. That's what caused me to start taking a more structured approach to chain maintenance. I'm not bragging. Road rash hurts.
For these reasons a simple chain checker is a wise investment. Amazon has 'em as low as $6. I check my chains every time I clean/lube them.