When you buy a new chain, it comes lubricated with a factory-installed grease-type lubricant. This lubricant is similar to hot wax. (Reliable sources — including Sheldon Brown, Shimano, and others — seem to agree that you should not deliberately remove this factory lube.)
Imagine that you own a low-end 21-speed bicycle, which you bought second-hand. You use it for commuting in a big city — in warm, dry weather only. You've bought and installed a brand-new chain. If you never clean or lubricate your chain, what will happen?
(In my experience, the bike seems to keep working for numerous miles without squeaking. But I wonder what's really going on behind the scenes, and what the results might be.)
Please assume that you do replace the chain whenever it's stretched by more than 0.5% (1/16"), and that you complete most other recommended bike maintenance on schedule. The only maintenance you skip is chain cleaning and lubrication.