In the new Google Places Dashboard, businesses can now delete listings.
The dashboard was first announced back in early April. Since then, it has been updated a number of times with various features and improvements. This Google forum post chronicles the updates as they were made.
Google's Jade Wang made note of the news about listing removals in a Google+ post on Monday:
Remove a listing now available for new Places dashboard users
From our forum post (http://goo.gl/A4mM2 )
Users of the new Places dashboard can now remove listings from their accounts (http://goo.gl/SwxLvO). Please note, you cannot undo removing a listing from your account.
If your business is closing, make sure you first report it as closed using Report a Problem (http://goo.gl/lGwPSS). If you'd also like to remove the business from displaying in your dashboard, first access the dashboard for the business you wish to remove. Select the Gear icon, then select Remove this listing.
Note that Google may continue to show businesses that have been removed from your account on Google Maps, Search, and other Google properties as closed, moved, or open, depending on the information we’ve received about the business.