The natural English language inclination would be to call the bricks (and other pieces) "Legos", but to trademark lawyers, trademarks are always to be used as attributive modifiers, not nouns. For this reason, the Lego company produced a famous warning not just on their web site, but long before the web existed. It was printed on the little catalogs that came in our sets:
The note said:
Dear Parents and Children
LEGO® is a brand name that is very special to all of us in the LEGO Group Companies. We would sincerely appreciate your help in keeping it special by referring to our bricks as "LEGO Bricks or Toys" and not just "LEGOS". By doing so, you will be helping to protect and preserve a brand that stands for quality the world over.
If at any time we can be of service to you regarding our products, please feel free to write to us.
Susan Williams
"Susan Williams" was a fiction, the personification of the Customer Affairs department — but, as if she were Santa Claus, in those days Lego always acted if she were very much real. If you wrote a letter to Lego and got a response, "she" signed it (see this example of a Susan Williams letter). So, it was a personal request. And it was a request from a person representing a company we all loved, because we loved their product.
So, when the sort of enthusiastic children who loved Lego so much that they read the fine print of the catalog and wrote letters to the company, we took the admonishment very seriously — but, I think, generally missed the point. Not being trademark lawyers, the message didn't read as "call them bricks or toys, not lego" — it was "don't call them legos!" So, we grew up with that warning in our minds, carefully playing with lego even as we casually blew our noses on kleenexes and tossed our unwanted xeroxes in dumpsters.
For this reason, the Lego vs. Legos debate has become a sort of shibboleth for the fan community. It's a signifier that the person you're talking to either grew up as one of those geeky fans, or is tied into the loose network of builders, makers, and artists for whom Lego is a passion. In many ways the technical correctness (or hyper-correctness) isn't as important as this cultural implication.