A few weeks ago my husband emailed LEGO because a piece was missing from a brand new set, and they popped the replacement in the mail straight a way. It was brilliant service. It turns out though that they will also do it for other sets, like say you bought one from eBay and found a missing piece. Just get in touch and they'll send you a free replacement.
LEGO do keep track, however, of who uses the service, so you wouldn't be able to request 900 pieces to build an uber construction for free. (Unless you supply them 450-odd emails and names and addresses over a period of years, in which case you probably deserve it.)
If you approach LEGO for free pieces once, you'll be sent them out, but if you ask again, you may be asked for the product number on the insert page (the map, my daughter calls it!) to verify that you actually own the set.
Like a puzzle with missing pieces though, it's a royal pain to get to the end of your construction and find a part is missing, so this is a really useful and helpful service when used correctly.
Click here for the free replacement service from Lego*
Thanks to goonertillidie at HUKD