If you buy and install a brand-new chain, but never clean or lubricate it, what will happen? 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 &mdash; including Sheldon Brown, Shimano, and others &mdash; 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 &mdash; 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.
Higher friction (comparing to properly lubricated chain) between chain pin and inner plate will make groove in pin surface faster, resulting in chain prolongation (a.k.a. chain "stretching").
Non-lubricated chain will be more exposed to corrosion.
Higher friction between the chain rollers and the chainrings will make the chainrings wear down faster.
Higher friction between all chain components will add avoidable resistance.
People on the street will look at you with embarrassment and compassion because of noise.